Question

$f:R\to R\mathrm{given}\mathrm{by}f\left(x\right)=x+\sqrt{x^2}\mathrm{is}$
(a) injective
(b) surjective
(c) bijective
(d) None of these

Answer 1

$$\begin{gathered} f\left(x\right)=x+\sqrt{x^2}=x\pm x=0\text{or}2x \\ \text{⇒ Each element of the domain has 2 images.} \end{gathered}$$
$\Rightarrow$f is not a function.
So, the answer is (d).