Let $f (x)$ be a function whose domain is $[- 5, 7]$
Let $g (x) = | 2 x + 5 |$ . Then the domain of $(f o g) (x)$ is

[- 5, 1]

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[- 4, 0]

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[- 6, 1]

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none of these

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Solution

The correct option is C $[- 6, 1]$
We have, $g (x) = | 2 x + 5 |$ .

The domain of $f (x)$ is $[- 5, 7]$ .

For $f (g (x))$ to exist, $- 5 \leq | 2 x + 5 | \leq 7$

$| 2 x + 5 |$ is always positive.

Hence, $| 2 x + 5 | \leq 7$

$\Rightarrow - 7 \leq 2 x + 5 \leq 7$

$\Rightarrow - 12 \leq 2 x \leq 2$

$\Rightarrow - 6 \leq x \leq 1$

Hence, option C is correct

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