Prove that

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,

$f^{-1}(10)=\sqrt{10-1}=\sqrt{9}=3$

 

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