Write whether f : R → R, given by


Write whether $f: R \rightarrow R$, given by $f(x)=x+\sqrt{x^{2}}$, is one-one, many-one, onto or into.


$f(x)=x+\sqrt{x^{2}}=x \pm x=0$ or $2 x$

So, each element $x$ in the domain may contain 2 images.

For example,



Here, the image of 0 and $-1$ is 0 .

Hence, $f$ is may-one.

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