Question

The function $\mathrm{f}\left(\mathrm{x}\right)={\mathrm{x}}^4+7$ is an

• A. Even function
• B. Odd function
• C. Neither even nor odd
• D. None of these

Answer 1

The correct option is A

Even function

Identify whether $\mathrm{f}\left(\mathrm{x}\right)$ is odd, even, or neither even nor odd

The function $\mathrm{f}\left(\mathrm{x}\right)$ is called an even function if $\mathrm{f}(-\mathrm{x})=\mathrm{x}$for all real values of $\mathrm{x}$.

Given function:

$\begin{array}{rcl}\mathrm{f}\left(\mathrm{x}\right)& =& {\mathrm{x}}^4+7\\ \mathrm{f}(-\mathrm{x})& =& {(-\mathrm{x})}^4+7\\ \mathrm{f}(-\mathrm{x})& =& {\mathrm{x}}^4+7\\ \because \mathrm{f}\left(-\mathrm{x}\right)& =& \mathrm{f}\left(\mathrm{x}\right)\end{array}$

$\therefore \mathrm{f}\left(\mathrm{x}\right)={\mathrm{x}}^4+7$ is an even function.

Hence, the correct option is A