Question

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

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

Answer 1

Answer: (A)

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