The range of the function $f (x) = | x^{2} + 2 x - 15 |$ is

R

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R^{+}

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R - {0}

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[0, \infty)

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Solution

The correct option is D $[0, \infty)$
Clearly, domain of $f$ is $R$ .
$x^{2} + 2 x - 15 = (x + 1)^{2} - 16$
$\Rightarrow - 16 \leq x^{2} + 2 x - 15 < \infty$
$\Rightarrow 0 \leq | x^{2} + 2 x - 15 | < \infty$

Hence, range of $f$ is $[0, \infty)$

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