The domain of the function cos-1 (2x - 1) is:

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Solution

Q.
The domain of the function $\cos^{- 1} (2 x - 1)$ is:

1 $[0, 1]$

2 $[- 1, 1]$

3 $(- 1, 1)$

4 $[0, π]$

Ans.
(1)

Ans. [0, 1]

Explanation:

We know that $\cos^{- 1} x$ is defined for $x \in [- 1, 1]$

$∴$ $f (x) = \cos^{- 1} (2 x - 1)$ is defined if

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

$\Rightarrow$    $0 \leq 2 x \leq 2$

$\Rightarrow$    $0 \leq x \leq 1$

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