Question:
Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be the function defined by $f(x)=4 x-3$ for all $x \in \mathbf{R}$. Then write $f^{-1}$.
Solution:
We have,
$f: \mathbf{R} \rightarrow \mathbf{R}$ is the function defined by $f(x)=4 x-3$ for all $x \in \mathbf{R}$
Let $f(x)=y$. Then,
$y=4 x-3$
$\Rightarrow 4 x=y+3$
$\Rightarrow x=\frac{y+3}{4}$
So, $f^{-1}(y)=\frac{y+3}{4}$
or, $f^{-1}(x)=\frac{x+3}{4}$