f : R→R given by
Question:

$f: R \rightarrow R$ given by $f(x)=x+\sqrt{x^{2}}$ is

(a) injective

(b) surjective

(c) bijective

(d) None of these

Solution:

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

$\Rightarrow$ Each element of the domain has 2 images.

$\Rightarrow f$ is not a function.

So, the answer is (d).

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