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Range

If a function...

Question

If a function $f : [- 2, \infty) \to R$ is such that $f (x) = x^{2} + 4 x - | x^{2} - 4 |,$ then the value(s) $f (x)$ can have is (are)

A

- 6

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B

- 8

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C

4

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D

0

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Solution

The correct option is D $0$
$f (x) = {\begin{matrix} 2 x^{2} + 4 x - 4, & x \in [- 2, 2] 4 x + 4, & x \in (2, \infty) \end{matrix}$

So, range $= [- 6, \infty)$

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