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Recent questions tagged functions

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1
Answer the questions on the basis of the information given below: $f_{1}(x) = \left\{\begin{matrix} x & 0 \leq x \leq 1 \\ 1 & x \geq 1 \\ 0 & \text{otherwise} \end{matrix}\right.$ $f_{2}(x) = f_{1}(-x) \;\; \text{for all} \; x $ ... $f_2(-x) = f_4(x) \: \text{for all }\;x$ $f_1(x) + f_3(x) = 0 \: \text{for all }\;x$
asked Mar 30 in Quantitative Aptitude Lakshman Patel RJIT 10.7k points 119 744 834 36 views
1 vote
1 answer
2
If $f(x) = x^{2} – 7x$ and $g(x) = x + 3,$ then the minimum value of $f(g(x)) – 3x$ is $ -16$ $ -15$ $ -20$ $ -12$
asked Jan 20 in Quantitative Aptitude soujanyareddy13 2.7k points 5 88 353 59 views
1 vote
1 answer
3
For all real values of $x,$ the range of the function $f(x) = \dfrac{x^{2} + 2x + 4}{2x^{2} + 4x + 9}$ is $ \left(\frac{3}{7}, \frac{1}{2} \right)$ $ \left[\frac{3}{7}, \frac{1}{2} \right)$ $ \left[\frac{3}{7}, \frac{8}{9} \right)$ $ \left[\frac{4}{9}, \frac{8}{9} \right]$
asked Jan 20 in Quantitative Aptitude soujanyareddy13 2.7k points 5 88 353 67 views
1 vote
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4
$f(x) = \dfrac{x^{2} + 2x – 15}{x^{2} – 7x – 18}$ is negative if and only if $ – 2 < x < 3 \; \text{or} \; x > 9 $ $ x < – 5 \; \text{or} \; 3 < x < 9 $ $ – 5 < x < – 2 \; \text{or} \; 3 < x < 9 $ $ x < – 5 \; \text{or} \; – 2 < x < 3 $
asked Jan 19 in Quantitative Aptitude soujanyareddy13 2.7k points 5 88 353 59 views
1 vote
1 answer
5
If $ f(x+y) = f(x) f(y) $ and $ f(5) = 4,$ then $ f(10) – f(-10) $ is equal to $0$ $15.9375$ $3$ $14.0625$
asked Sep 17, 2021 in Quantitative Aptitude soujanyareddy13 2.7k points 5 88 353 129 views
2 votes
1 answer
6
Let $f(x) = x^{2} + ax + b $ and $g(x) = f(x+1) – f(x-1).$ If $ f(x) \geq 0 $ for all real $x,$ and $ g(20) = 72,$ then the smallest possible value of $b$ is $1$ $16$ $0$ $4$
asked Sep 17, 2021 in Quantitative Aptitude soujanyareddy13 2.7k points 5 88 353 89 views
1 vote
1 answer
7
If $f\left ( 5+x \right )= f\left ( 5-x \right )$ for every real $x,$ and $f\left ( x \right )=0$ has four distinct real roots, then the sum of these roots is $0$ $40$ $10$ $20$
asked Sep 16, 2021 in Quantitative Aptitude soujanyareddy13 2.7k points 5 88 353 110 views
1 vote
1 answer
8
Let $f$ be a function such that $f (mn) = f (m) f (n)$ for every positive integers $m$ and $n$. If $f (1), f (2)$ and $f (3)$ are positive integers, $f (1) < f (2),$ and $f (24) = 54$, then $f (18)$ equals _______
asked Mar 20, 2020 in Quantitative Aptitude go_editor 13.3k points 309 2254 2467 181 views
2 votes
1 answer
9
If $f(x+2)=f(x)+f(x+1)$ for all positive integers $x$, and $f(11)=91,f(15)=617$, then $f(10)$ equals ________
asked Mar 20, 2020 in Quantitative Aptitude go_editor 13.3k points 309 2254 2467 196 views
1 vote
1 answer
10
Let $f\left ( x \right )=x^{2}$ and $g\left ( x \right )=2^{x}$, for all real $x$. Then the value of $ f \left ( f\left ( g\left ( x \right ) \right )+g\left( f\left ( x \right ) \right ) \right)$ at $x=1$ is $16$ $18$ $36$ $40$
asked Mar 16, 2020 in Quantitative Aptitude go_editor 13.3k points 309 2254 2467 153 views
1 vote
1 answer
11
Let $f\left ( x \right )=2x-5$ and $g\left ( x \right )=7-2x.$ Then $ \mid f\left ( x \right ) + g\left ( x \right ) \mid=\mid f(x) \mid + \mid g\left ( x \right ) \mid$ if and only if $5/2<x<7/2$ $x\leq 5/2$ or $x\geq 7/2$ $x< 5/2$ or $x\geq 7/2$ $5/2\leq x\leq 7/2$
asked Mar 16, 2020 in Quantitative Aptitude go_editor 13.3k points 309 2254 2467 192 views
1 vote
1 answer
12
If $f\left ( ab \right )=f\left ( a \right )f\left ( b \right )$ for all positive integers $a$ and $b$, then the largest possible value of $f\left (1\right )$ is $1$ $2$ $0$ $3$
asked Mar 16, 2020 in Quantitative Aptitude go_editor 13.3k points 309 2254 2467 125 views
1 vote
1 answer
13
If $f( x)=\dfrac{5x+2}{ 3x-5}$ and $g( x )=x^{2}-2x-1,$ then the value of $g( f( f( 3 ) ) )$ is $2$ $1/3$ $6$ $2/3$
asked Mar 13, 2020 in Quantitative Aptitude go_editor 13.3k points 309 2254 2467 142 views
1 vote
1 answer
14
$A, S, M$ and $D$ are functions of $x$ and $y$, and they are defined as follows. $A(x, y) = x + y$ $M(x, y) = xy$ $S(x,y)= x-y$ $D(x,y)= x/y, y\neq 0$ What is the value of $M(M(A(M(x, y), S(y, x)), x), A(y, x))$ for $x = 2, y = 3$? $60$ $140$ $25$ $70$
asked Mar 11, 2020 in Quantitative Aptitude go_editor 13.3k points 309 2254 2467 262 views
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15
The set of all positive integers is the union of two disjoint subsets$:\left \{ f\left ( 1 \right ),f\left ( 2 \right ), \dots, f\left ( n \right ), \dots \right \}$ and $\left \{ g\left ( 1 \right ),g\left ( 2 \right ), \dots, g\left ( n \right ), \dots \right \}$, ... $n \geq 1$. What is the value of $g\left ( 1 \right )?$ $0$ $2$ $1$ Cannot be determined
asked Mar 9, 2020 in Quantitative Aptitude go_editor 13.3k points 309 2254 2467 189 views
1 vote
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16
For all non-negative integers $x$ and $y$, $f(x,y)$ is defined as below. $f( 0,y) = y+1$ $f(x+1,0) = f( x, 1)$ $f( x+1, y+1) = f\left( x,f( x+1,y) \right)$ Then what is the value of $f(1,2)$ ________
asked Mar 9, 2020 in Quantitative Aptitude go_editor 13.3k points 309 2254 2467 1.9k views
1 vote
1 answer
17
$\begin{array}{}Let\;f_{n+1}(x)&=f_n(x)+1\;\text{if $n$ is a multiple of 3}\\ &=f_n(x)-1\;\text{otherwise.}\end{array}$ If $f_1(1)=0$, then what is $f_{50}(1)$? $-18$ $-16$ $-17$ Cannot be determined
asked Mar 9, 2020 in Quantitative Aptitude Krithiga2101 268 points 6 53 68 262 views
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18
Consider the function given by $f(x) =\mid x-1\mid-x$ What is the area of the triangle bounded by the graph of the given function with the coordinate axis given by $x=0\:\text{and}\:y=0$? $2$ $\large\frac{1}{4}$ $\large\frac{1}{2}$ $1$
asked Mar 9, 2020 in Quantitative Aptitude Krithiga2101 268 points 6 53 68 172 views
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19
The graphs given alongside represent two functions $f(x)\:\text{and}\:g(x)$ respectively. Which of the following is true? $g(x)=[f(x)]$ $g(x)=f(-x)$ $g(x)=-f(x)$ None of these
asked Mar 9, 2020 in Quantitative Aptitude Krithiga2101 268 points 6 53 68 167 views
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20
Consider the function given by $f(x) =\mid x-1\mid-x$ Which of the following is not true about the graph of $f(x)$? A portion of the graph is parallel to the line $y = 25$. A portion of graph is in 2nd quadrant. Some portion of graph lies in 1st quadrant. Some portion of graph lies in 3rd quadrant.
asked Mar 9, 2020 in Quantitative Aptitude Krithiga2101 268 points 6 53 68 170 views
1 vote
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21
For any positive integer $n$, let $f(n)=n(n+1)$ if n is even, and $f(n)=n+3$ if n is odd. if $m$ is a positive integer such that $8f(m+1)-f(m)=2$, then $m$ equals _______
asked Mar 8, 2020 in Quantitative Aptitude go_editor 13.3k points 309 2254 2467 246 views
1 vote
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22
Consider a function $f$ satisfying $f(x+y)=f(x)f(y)$ where $x,y$ are positive integers, and $f(1)=2$. If $f(a+1)+f(a+2)+\ldots +f(a+n)=16(2^{n}-1)$ then $a$ is equal to ______
asked Mar 8, 2020 in Quantitative Aptitude go_editor 13.3k points 309 2254 2467 159 views
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23
If $g(x)=p\mid x \mid-qx^2$, where $p$ and $q$ are constants, then at $x=0, g(x)$ will be maximum when $p>0,q>0$ minimum when $p<0,q<0$ minimum when $p>0,q<0$ maximum when $p>0,q<0$
asked Mar 6, 2020 in Quantitative Aptitude admin 2.4k points 87 175 237 208 views
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24
Let $f(x)= \dfrac{1}{1+x^2}$ and $g(x)=\dfrac{e^{−x}}{1+[x]}$, where $[x]$ is the greatest integer less than or equal to $x$. Then which of the following domain is true? domain of $(f+g)=R-(-2,-1]$ domain of $(f+g)=R-[-1,0)$ ... Both II and IV Both I and III Both I and IV Both II and III
asked Mar 6, 2020 in Quantitative Aptitude admin 2.4k points 87 175 237 157 views
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25
Let $f$ be an injective map with domain $\left \{ x, y, z \right \}$ and the range $\left \{ 1, 2, 3 \right \}$ such that exactly one of the following statements is correct and the remaining are false. $f\left \{x \right \}=1,f\left ( y \right )\neq 1,f\left ( z \right )\neq 2.$ The value of $f^{-1}\left ( 1 \right )$ is $x$ $y$ $z$ None of the above
asked Mar 1, 2020 in Quantitative Aptitude Arjun 8.3k points 55 131 178 122 views
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26
Answer the question based on the information given below: Let x and y be real numbers and let $f(x, y) = |x+y|, F(f(x, y)) = -f(x,y) \text{ and } G(f(x, y)) = -F(f(x, y))$ Which of the following expressions yields $x^2$ as a result? $F(f(x, -x)).G(f(x, -x))$ $F(f(x, x)).G(f(x, x)).4$ $-F(f(x, x)).G(f(x, -x)) \: \log_2 16$ $f(x,x).f(x,x)$
asked May 14, 2016 in Logical Reasoning go_editor 13.3k points 309 2254 2467 246 views
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27
Answer the question based on the information given below: Let x and y be real numbers and let $f(x, y) = |x+y|, F(f(x, y)) = -f(x,y) \text{ and } G(f(x, y)) = -F(f(x, y))$ Which of the following statements is true? $F(f(x,y)) .G(f(x,y)) = -F(f(x,y)).G(f(x,y))$ $F(f(x,y)) .G(f(x,y)) > -F(f(x,y)).G(f(x,y))$ $F(f(x,y)) .G(f(x,y)) \neq G(f(x,y)).F(f(x,y))$ $F(f(x,y)) +G(f(x,y)) + f(x,y)= f(-x,-y)$
asked May 14, 2016 in Logical Reasoning go_editor 13.3k points 309 2254 2467 277 views
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28
Answer the following question based on the information given below. For real numbers $x, y,$ let $f(x, y) = \left\{\begin{matrix} \text{Positive square-root of}\; (x + y),\;\text{if}\; (x + y)^{0.5}\;\text{is real} \\ (x + y)^2,\;\text{otherwise} \end{matrix}\right.$ ... than $g(x, y)?$ Both $x$ and $y$ are less than $-1$ Both $x$ and $y$ are positive Both $x$ and $y$ are negative $y > x$
asked May 1, 2016 in Quantitative Aptitude go_editor 13.3k points 309 2254 2467 392 views
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29
Answer the following question based on the information given below. For three distinct real numbers $x, y$ and $z,$ let $f(x, y, z) = \min(\max(x, y), \max(y, z), \max(z, x))$ $g(x, y, z) = \max(\min(x, y), \min(y, z), \min(z, x))$ $h(x, y, z) = \max(\max(x, y), \max(y, z), \max(z, x))$ ... $(h(x, y, z) - f(x, y, z))/(n(x, y, z) - g(x, y, z))$
asked May 1, 2016 in Quantitative Aptitude go_editor 13.3k points 309 2254 2467 230 views
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30
Answer the following question based on the information given below. For three distinct real numbers $x, y$ and $z,$ let $f(x, y, z) = \min(\max(x, y), \max(y, z), \max(z, x))$ $g(x, y, z) = \max(\min(x, y), \min(y, z), \min(z, x))$ $h(x, y, z) = \max(\max(x, y), \max(y, z), \max(z, x))$ ... $(j(x, y, z) - g(x, y, z))/h(x, y, z)$ $(f(x, y, z) - h(x, y, z))/f(x, y, z)$
asked May 1, 2016 in Quantitative Aptitude go_editor 13.3k points 309 2254 2467 673 views
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31
Use the following information for next two questions: A function $f(x)$ is said to be even if $f(-x) = f(x)$, and odd if $f(-x) = -f(x)$. Thus, for example, the function given by $f(x)=x^{2}$ is even, while the function given by ... following questions. The sum of two odd functions is always an even function is always an odd function is sometimes odd and sometimes even may be neither odd nor even
asked Apr 27, 2016 in Quantitative Aptitude go_editor 13.3k points 309 2254 2467 358 views
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32
Answer the following question based on the information given below. For a real number $x,$ let f(x) = 1/(1 + x), if x is non-negative = 1+ x, if x is negative f$^n$(x) = f(f$^{n – 1}$(x)), n = 2, 3, .... $r$ is an integer $\geq 2.$ Then what is the value of $f^{r-1}(-r) + f^r(-r)+f^{r+1}(-r)$? $-1$ $0$ $1$ None of these
asked Apr 25, 2016 in Quantitative Aptitude go_editor 13.3k points 309 2254 2467 170 views
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33
Answer the following question based on the information given below. Given below is a graph made up of straight-line segments shown as thick lines. Choose the answer as if $f(x) = 3 f(–x);$ if $f(x) = –f(–x);$ if $f(x) = f(–x);$ and if $3 f(x) = 6 f(–x),$ for $x\geq 0.$ $1$ $2$ $3$ $4$
asked Apr 25, 2016 in Quantitative Aptitude go_editor 13.3k points 309 2254 2467 219 views
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34
Answer the following question based on the information given below. Given below is a graph made up of straight-line segments shown as thick lines. Choose the answer as if $f(x) = 3 f(–x);$ if $f(x) = –f(–x);$ if $f(x) = f(–x);$ and if $3 f(x) = 6 f(–x),$ for $x\geq 0.$ $1$ $2$ $3$ $4$
asked Apr 25, 2016 in Quantitative Aptitude go_editor 13.3k points 309 2254 2467 174 views
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35
For all non-negative integers $x$ and $y, f(x, y)$ is defined as below $f(0, y) = y + 1$ $f(x + 1, 0) = f(x, 1)$ $f(x + 1,y + 1) = f(x, f(x + 1, y))$ Then, what is the value of $f(1, 2)?$ Two Four Three Cannot be determined
asked Mar 30, 2016 in Quantitative Aptitude go_editor 13.3k points 309 2254 2467 288 views
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36
The set of all positive integers is the union of two disjoint subsets $\{f(1), f(2),\dots ,f(n),\dots\}$ and $\{g(1), g(2),\dots,g(n),\dots\},$ where $f(1) < f(2) <\dots < f(n) < \dots,$ and $g(1) < g(2) <\dots< g(n) < \dots,$ and $g(n) = f(f(n)) + 1$ for all $n \geq 1.$ What is the value of $g(1)?$ Zero Two One Cannot be determined
asked Mar 30, 2016 in Quantitative Aptitude go_editor 13.3k points 309 2254 2467 666 views
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37
Answer the following question based on the information given below. For a real number $x$, let f(x) = 1/(1 + x), if x is non-negative = 1+ x, if x is negative f$^n$(x) = f(f$^{n – 1}$(x)), n = 2, 3, .... What is the value of the product, $f(2)f^2(2)f^3(2)f^4(2)f^5(2)$? $\frac{1}{3}$ $3$ $\frac{1}{18}$ None of these
asked Mar 29, 2016 in Quantitative Aptitude go_editor 13.3k points 309 2254 2467 140 views
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38
Answer the following question based on the information given below. Given below is a graph made up of straight-line segments shown as thick lines. Choose the answer as if $f(x) = 3 f(–x);$ if $f(x) = –f(–x);$ if $f(x) = f(–x);$ and if $3 f(x) = 6 f(–x),$ for $x\geq 0.$ $1$ $2$ $3$ $4$
asked Mar 29, 2016 in Quantitative Aptitude go_editor 13.3k points 309 2254 2467 134 views
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39
Answer the following question based on the information given below. For three distinct real numbers $x, y$ and $z,$ let $f(x, y, z) = \min(\max(x, y), \max(y, z), \max(z, x))$ $g(x, y, z) = \max(\min(x, y), \min(y, z), \min(z, x))$ $h(x, y, z) = \max(\max(x, y), \max(y, z), \max(z, x))$ ... $j(x, y, z)/h(x, y, z)$ $f(x, y, z)/g(x, y, z)$ $(f(x, y, z) + h(x, y, z) - g(x, y, z))/j(x, y, z)$
asked Mar 29, 2016 in Quantitative Aptitude go_editor 13.3k points 309 2254 2467 169 views
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40
Answer the following question based on the information given below. For real numbers $x, y,$ let $f(x, y) = \left\{\begin{matrix} \text{Positive square-root of}\; (x + y),\;\text{if}\; (x + y)^{0.5}\;\text{is real} \\ (x + y)^2,\;\text{otherwise} \end{matrix}\right.$ ... $f(x, y) - (g(x, y))^2$ $g(x, y) - (f(x, y))^2$ $f(x, y) + g(x, y)$
asked Mar 29, 2016 in Quantitative Aptitude go_editor 13.3k points 309 2254 2467 216 views
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