CAT 2014 | Question: 33

Question

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 $f(x)=x^{3}$ is odd. Using this definition, answer the following questions.

The sum of two odd functions 

• A. is always an even function
• B. is always an odd function 
• C. is sometimes odd and sometimes even
• D. may be neither odd nor even

Answer 1

the answer is always an odd function........

let f(x) and g(x) be two odd functions

then h(x) = f(x)+g(x) => h(-x) = -f(x)-g(x) =-(f(x)+g(x)) =-h(x)

which clearly indicates that h(x) is an odd function

Comments

what if h(x) is zero? i.e. f(x)=-g(x)