The domain of the function f(x) = sin^-1(2x-3), is

The domain of $sin^{-1}$ x is [-1,1]. Therefore, $f(x) = sin^{-1}(2x-3)$ is defined for all x satisfying

$-1 ≤ 2x - 3 ≤ 1 ⇒ 3-1 ≤ 2x ≤ 3+1 ⇒1 ≤ x ≤ 2 ⇒ x ∈ [1,2]$

Hence, domain of f(x) = $sin^{-1}(2x-3) $ is [1,2]