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Domain

Given that gx...

Question

Given that $g (x) = [f (x) - 1]^{2}$ . Find the domain of f(x) = 1 - 2x, given that $0 \leq g (x) < 4$ .

$[- 1, 3)$

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$(- 1, \frac{1}{2})$

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$- 1, 1$

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$(- 3, 1]$

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Solution

The correct option is C
$- 1, 1$

Given that $g (x) = [f (x) - 1]^{2}$
$0 \leq g (x) < 4 \Rightarrow 0 \leq [f (x) - 1]^{2} < 4 \Rightarrow - 2 < f (x) - 1 < 2$
Substitute f(x) = 1-2x
$- 2 < - 2 x < 2 \Rightarrow 1 > x > - 1$
Therefore, the domain of f(x) is (-1, 1).

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