Question

$f\left(x\right)=\frac{a^{-x}+a^x}{2}+\cos x$ is

• A. an odd function.
• B. an even function.
• C. neither odd nor even function.
• D. both odd nor even function.

Answer 1

The correct option is B an even function.

Let $f\left(x\right)=f_1\left(x\right)+f_2\left(x\right)$
Where
$f_1\left(x\right)=\frac{a^{-x}+a^x}{2}{f}_2\left(x\right)=\cos x$
We know that
$f_1\left(x\right),f_2\left(x\right)$ are even functions, so the sum of even functions is even.
Therefore, $f\left(x\right)$ is even function.