CAT 2014 | Question: 32

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 function given by $f(x) = |x|^{3}$

• A. even 
• B. odd 
• C. neither 
• D. both

Answer 1

Given that, $f(-x) = \left\{\begin{matrix} f(x) ;  & even  \\ -f(-x) ; & odd  \end{matrix}\right.$

$f(x) = |x|^{3} \longrightarrow (1)$

We know that $f(x) = |x| = x $

$\qquad f(-x) = |-x| = x $

So, $f(x) = |x| $ is even function.

Now, $f(x) = |x|^{3}$

$\Rightarrow \boxed{f(x) = x^{3} (odd)}$

Correct Answer $: \text{B}$