Let $f: \mathbb{R} \to \mathbb{R}$ be the function defined by $f(x) = 2x - 3, \forall x \in \mathbb{R}$. Write $f^{-1}$.

$f^{-1}(x) = \frac{x + 3}{2}$

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

$y = 2x - 3$

$2x = y + 3$

$x = \frac{y + 3}{2}$

$∴f^{-1}(x) = \frac{x + 3}{2}$