Question:
Let $f: R \rightarrow R: f(x)=10 x+3$. Find $f^{-1}$.
Solution:
To find: $\mathrm{f}^{-1}$
Given: $f: R \rightarrow R: f(x)=10 x+3$
We have,
$f(x)=10 x+3$
Let $f(x)=y$ such that $y \in R$
$\Rightarrow y=10 x+3$
$\Rightarrow y-3=10 x$
$\Rightarrow x=\frac{y-3}{10}$
$\Rightarrow f^{-1}=\frac{y-3}{10}$
Ans) $f^{-1}(y)=\frac{y-3}{10}$ for all $y \in R$
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