Find the domain of $f (2 x - 1)$ if the domain of $f (x) i s [- 1, 1]$

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Solution

Since the domain of $f (x) i s [- 1, 1]$
$\Rightarrow$ x $\in$ $[- 1, 1]$

Even if we write it as $f (y), y \in [- 1, 1] .$
In the case of $f (2 x - 1) (2 x - 1) \in [- 1, 1]$

$- 1 \leq 2 x - 1 \leq 1$
$0 \leq 2 x \leq 2$
$0 \leq x \leq 1$

$\Rightarrow x \in [0, 1]$

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