Question:
Let $\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R}: \mathrm{f}(\mathrm{x})=\frac{2 \mathrm{x}-7}{4}$ be an invertible function. Find $\mathrm{f}^{-1}$.
Solution:
To find: $\mathrm{f}^{-1}$
Given: $f: R \rightarrow R: f(x)=\frac{2 x-7}{4}$
We have,
$f(x)=\frac{2 x-7}{4}$
Let $f(x)=y$ such that $y \in R$
$\Rightarrow y=\frac{2 x-7}{4}$
$\Rightarrow 4 y=2 x-7$
$\Rightarrow 4 y+7=2 x$
$\Rightarrow x=\frac{4 y+7}{2}$
$\Rightarrow f^{-1}=\frac{4 y+7}{2}$
Ans) $f^{-1}(y)=\frac{4 y+7}{2}$ for all $y \in R$