Question: Let $f: R \rightarrow R: f(x)=x^{2}+1$. Find $f^{-1}\{10\}$
Solution:
Given:
$f: R \rightarrow R: f(x)=x^{2}+1$
To find inverse of $f(x)$
Let $y=f(x)$
$y=x^{2}+1$
$y-1=x^{2}$
$\mathrm{x}=\sqrt{y-1}$
$f^{-1}(x)=\sqrt{x-1}$
Substituting x = 10,
$f^{-1}(10)=\sqrt{10-1}=\sqrt{9}=3$
