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  4. The function f(x)=(x/ex-1)+(x/2)+1 is

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Q. The function $f(x)=\frac{x}{e^x-1}+\frac{x}{2}+1$ is

Relations and Functions

Solution:

$f(-x)=\frac{-x}{e^x-1}-\frac{x}{2}+1 $
$ =\frac{-x e^x}{1-e^x}-\frac{x}{2}+1$
$=\frac{x\left(e^x-1+1\right)}{e^x-1}-\frac{x}{2}+1 $
$=\frac{x}{e^x-1}+\frac{x}{2}+1=f(x)$