Question

$f\left(x\right)=x\frac{e^x+1}{e^x-1}$ is an even function.

• A. True
• B. False

Answer 1

The correct option is A True

Given the function $f\left(x\right)=x\frac{e^x+1}{e^x-1}$.

Now $f(-x)=(-x)\frac{e^{-x}+1}{e^{-x}-1}=x\frac{e^x+1}{e^x-1}=f\left(x\right)\forall x$.

So $f(-x)=f\left(x\right)\forall x$.

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