Question

If $f:R\to R$ is defined by $f\left(x\right)=\left|x\right|$, then:

• A. $f^{-1}\left(x\right)=-x$
• B. $f^{-1}\left(x\right)=\frac{1}{\left|x\right|}$
• C. $f^{-1}\left(x\right)$ does not exist
• D. $f^{-1}\left(x\right)=\frac{1}{x}$

Answer 1

Answer: (C)

$f^{-1}\left(x\right)$ does not exist

$f^{-1}\left(x\right)$ does not exist.
For $f^{-1}\left(x\right)=x$ to exists ,$f\left(x\right)$ must be subjective.But in case when $f\left(x\right)=\left|x\right|$ ,$f\left(x\right)$ is not injective(one-one).
Therefore $f^{-1}\left(x\right)$ does not exist.