Question

$f:R\to R,f\left(x\right)=\frac{x}{x^2+1}$ Show that function is neither one-one, nor onto.

Answer 1

We have

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

$f^{\prime }\left(x\right)=0$

$x=\pm 1$

Also from the graph $f\left(x\right)\in \left[-\frac{1}{2},\frac{1}{2}\right]$

Hence, from graph function is neither one one nor onto.