The domain of function ^ -1 (2 x-3) is : - Vidyadip

MCQ

The domain of function $\cos ^{-1}(2 x-3)$ is :

A
$[-1,1]$
B
$(1,2)$
C
(-1,1)
✓
$[1,2]$

✓

Answer

Correct option: D.

$[1,2]$

(D)
The domain of $\cos ^{-1}(\theta)$ is $-1 \leq \theta \leq 1$$
\begin{array}{ll}
\text { So, } & -1 \leq 2 x-3 \leq 1 \\
\Rightarrow & -1+3 \leq 2 x-3+3 \leq 1+3 \\
\Rightarrow & 2 \leq 2 x \leq 4 \\
\Rightarrow & 1 \leq x \leq 2 \\
\Rightarrow & x \in[1,2]
\end{array}
$
Hence correct option is (D).

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