Let $f: \mathbb{R} \to \mathbb{R}$ be the function defined by $f(x) = 2x - 3, \forall x \in \mathbb{R}$. Write $f^{-1}$.
Answer & explanation
Correct answer: option 2
The correct answer is Option (3) → $f^{-1}(x) = \frac{x + 3}{2}$ ##
Given that,
$f(x) = 2x - 3, \forall x \in \mathbb{R}$
Now, let
$y = 2x - 3$
$2x = y + 3$
$x = \frac{y + 3}{2}$
$∴f^{-1}(x) = \frac{x + 3}{2}$