Solve this


Let $\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R}: \mathrm{f}(\mathrm{x})=\frac{2 \mathrm{x}-7}{4}$ be an invertible function. Find $\mathrm{f}^{-1}$.



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 $y \in R$


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