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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