The domain and range of the function \( f(x)=2\cos^{-1}(2x-3) \) respectively are:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → [1, 2] and [0, 2π]
Domain: \( \cos^{-1} \) is defined only on [−1, 1], so
\( \displaystyle -1\le 2x-3\le 1 \)
\( \displaystyle 2\le 2x\le 4\ \Rightarrow\ 1\le x\le 2 \)
Range: \( \cos^{-1} \) takes every value in \( [0,\pi] \), so
\( \displaystyle 0\le 2\cos^{-1}(2x-3)\le 2\pi \)
So the domain is [1, 2] and the range is [0, 2π].