The range of the function $f(x)=\frac{x}{1+|x|}$ is

Question

Professor PC Thomas Classes · Answer

If $x$ is $>0$ then $f(x)=\frac{x}{1+x} f(x)$ lies between 0 and $1 \mathrm{f}(0)=0 . \mathrm{f}(\mathrm{x})$ is an odd function
∴ Range of f is $(-1,1)$