(A) We have the function $f(x) = \cos^{-1} \sqrt{x-1}$.For the function $\cos^{-1}(u)$ to be defined,the argument $u$ must satisfy $u \in [-1, 1]$.Sin

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(A) We have the function $f(x) = \cos^{-1} \sqrt{x-1}$.For the function $\cos^{-1}(u)$ to be defined,the argument $u$ must satisfy $u \in [-1, 1]$.Since $\sqrt{x-1}$ is always non-negative,the condition becomes $0 \leq \sqrt{x-1} \leq 1$.Squaring the inequality,we get $0 \leq x-1 \leq 1$.Adding $1$ to all parts,we obtain $1 \leq x \leq 2$.Therefore,the domain of $f(x)$ is $[1, 2]$.

Class 12 Mathematics Inverse Trigonometric Functions Domain and Range of ITF

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

KCET 2020 All KCET

A
$[1, 2]$
B
$[0, 2]$
C
$[-1, 1]$
D
$[0, 1]$

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