Find the value

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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