The function $f (x)$ is defined on the interval $[0, 1]$ . Find the domain of the function:
$f (2 x + 3)$

- \frac{3}{2} \leq x \leq - 1

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- \frac{3}{2} \leq x \leq \frac{3}{2}

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- 1 \leq x \leq \frac{3}{2}

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- 1 \leq x \leq 1

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Solution

The correct option is B $- \frac{3}{2} \leq x \leq - 1$
Given $f (x)$ defined in the interval $[0, 1]$
$∴ f (2 x + 3)$ defined if, $0 \leq 2 x + 3 \leq 1$
$\Rightarrow 0 - 3 \leq 2 x \leq 1 - 3$

$\Rightarrow - 3 \leq 2 x \leq - 2$
$\Rightarrow - \frac{3}{2} \leq x \leq - 1$

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