# Recent questions tagged functions

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Answer the questions on the basis of the information given below:$f_{1}(x) = \left\{\begin{matrix} x & 0 \leq x \leq 1 \\ 1 & x \geq 1 \\ 0 & \text{otherwise} \end{matri... 1 answer 2 If$f(x) = x^{2} – 7x$and$g(x) = x + 3,$then the minimum value of$f(g(x)) – 3x$is$ -16$$-15$$ -20$$-12 1 answer 3 For all real values of x, the range of the function f(x) = \dfrac{x^{2} + 2x + 4}{2x^{2} + 4x + 9} is \left(\frac{3}{7}, \frac{1}{2} \right)$$ \left[\frac{3}{7}, \fr...
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$f(x) = \dfrac{x^{2} + 2x – 15}{x^{2} – 7x – 18}$ is negative if and only if$– 2 < x < 3 \; \text{or} \; x 9 $$x < – 5 \; \text{or} \; 3 < x < 9$$ – 5 < x... 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$$14.0625 1 answer 6 Let f(x) = x^{2} + ax + b  and g(x) = f(x+1) – f(x-1). If  f(x) \geq 0  for all real x, and  g(20) = 72, then the smallest possible value of b is 1$$16$$0... 1 answer 7 If f\left ( 5+x \right )= f\left ( 5-x \right ) for every real x, and f\left ( x \right )=0 has four distinct real roots, then the sum of these roots is0$$40$$10$$...
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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 $... 1 answer 9 If$f(x+2)=f(x)+f(x+1)$for all positive integers$x$, and$f(11)=91,f(15)=617$, then$f(10)$equals ________ 1 answer 10 Let$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...
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Let $f\left ( x \right )=2x-5$ and $g\left ( x \right )=7-2x.$ Then $\mid f\left ( x \right ) + g\left ( x \right ) \mid=\mid f(x) \mid + \mid g\left ( x \right ) \mid$ ...
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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... 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$$2/3 1 answer 14 A, S, M and D are functions of x and y, and they are defined as follows.A(x, y) = x + y$$M(x, y) = xy$$S(x,y)= x-y$$D(x,y)= x/y, y\neq 0$What is the value of$M(...
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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 ...
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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)$Then what is the v...
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$\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$$-16$$... 0 answers 18 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)$None ... 0 answers 19 Consider the function given by$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\:\...
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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 $y = 25$....
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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 ______...
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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 _...
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If $g(x)=p\mid x \mid-qx^2$, where $p$ and $q$ are constants, then at $x=0, g(x)$ will bemaximum when $p>0,q>0$minimum when $p<0,q<0$minimum when $p>0,q<0$maximum when $p... 0 answers 24 Let$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$. Then which of the following domain is true... 0 answers 25 Let$f$be an injective map with domain$\left \{ x, y, z \right \}$and the range$\left \{ 1, 2, 3 \right \}$such that exactly one of the following statements is corre... 1 answer 26 Answer the question based on the information given below:Let x and y be real numbers and let$f(x, y) = |x+y|, F(f(x, y)) = -f(x,y) \text{ and } G(f(x, y)) = -F(f(x, y))$W... 1 answer 27 Answer the question based on the information given below:Let x and y be real numbers and let$f(x, y) = |x+y|, F(f(x, y)) = -f(x,y) \text{ and } G(f(x, y)) = -F(f(x, y))$W... 0 answers 28 Answer the following question based on the information given below.For real numbers$x, y,$let$f(x, y) = \left\{\begin{matrix} \text{Positive square-root of}\; (x + y),\...
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Answer the following question based on the information given below.For three distinct real numbers $x, y$ and $z,$ let$f(x, y, z) = \min(\max(x, y), \max(y, z), \max(z, x... 1 answer 30 Answer the following question based on the information given below.For three distinct real numbers$x, y$and$z,$let$f(x, y, z) = \min(\max(x, y), \max(y, z), \max(z, x...
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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 ...
Answer the following question based on the information given below.For a real number $x,$ letf(x)= 1/(1 + x),if x is non-negative = 1+ x,if x is negativef$^n$(x)= f(f$^{n... 0 answers 33 Answer the following question based on the information given below.Given below is a graph made up of straight-line segments shown as thick lines. Choose the answer asif$...
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 asif $... 0 answers 35 For all non-negative integers$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))$Then, what is the value ... 0 answers 36 The set of all positive integers is the union of two disjoint subsets$\{f(1), f(2),\dots ,f(n),\dots\}$and$\{g(1), g(2),\dots,g(n),\dots\},$where$f(1) < f(2) <\dots ...
Answer the following question based on the information given below.For a real number $x$, letf(x)= 1/(1 + x),if x is non-negative = 1+ x,if x is negativef$^n$(x)= f(f$^{n... 0 answers 38 Answer the following question based on the information given below.Given below is a graph made up of straight-line segments shown as thick lines. Choose the answer asif$...
Answer the following question based on the information given below.For three distinct real numbers $x, y$ and $z,$ let$f(x, y, z) = \min(\max(x, y), \max(y, z), \max(z, x... 0 answers 40 Answer the following question based on the information given below.For real numbers$x, y,$let$f(x, y) = \left\{\begin{matrix} \text{Positive square-root of}\; (x + y),\...