Question

The domain of the function defined by $f\left(x\right) = cos^{-1}\sqrt{x-1} $ is

• A. [1, 2]
• B. [0, 2]
• C. [-1, 1]
• D. [0, 1]

Answer 1

Answer: (A)

For $f$ to be defined,
$x-1 \geq 0$ and $-1 \leq \sqrt{(}(x-1) \leq 1$
$\Rightarrow x \geq 1$ and $0 \leq x -1 \leq 1$
$\Rightarrow x \geq 1$ and $1 \leq x \leq 2$
$\Rightarrow x \in[1,2]$
Hence, domain of $f$ is $[1,2]$.