f(x) = x + x^2 is a function from R R , then f(x) is - Vidyadip

MCQ

$f(x) = x + \sqrt {{x^2}} $ is a function from $R \to R$ , then $f(x)$ is

A
Injective
B
Surjective
C
Bijective
✓
None of these

✓

Answer

Correct option: D.

None of these

d
(d) We have $f(x) = x + \sqrt {{x^2}} = x + |x|$

Clearly f is not one-one as $f( - 1) = f( - 2) = 0$ but $ - 1 \ne 2$.

Also $f$ is not onto as $f(x) \ge 0,\,\forall x \in R,$

Also, range of $f = (0,\infty ) \subset R$.

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