Question

A function $f\left(x\right)$ is even if for all a $x$, $f(-x)=f\left(x\right)$, and odd if for all $x$, $f(-x)=-f\left(x\right)$.

If $f\left(x\right)=5x^6+6x^2+7$, which of the following is correct?

• A. $[-f(x\left)\right]$ is not even
• B. $f\left(x\right)$ is odd
• C. $[-f(x\left)\right]$ is not odd
• D. $f\left(x\right)$ is even

Answer 1

Answer: (D)

$f\left(x\right)$ is even

Given, $f\left(x\right)=5x^6+6x^2+7$

Therefore, $f(-x)=5{(-x)}^6+6{(-x)}^2+7$

$\Rightarrow f(-x)=5x^6+6x^2+7$

$\Rightarrow f\left(x\right)=f(-x)$

So $f\left(x\right)$ is an even function.

Option D is correct.