KCET · Maths · Functions
If \(f: R \rightarrow R\) is defined by \(f(x)=|x|\), then
- A \(f^{-1}(x)=-x\)
- B \(f^{-1}(x)=\frac{1}{|x|}\)
- C the function \(f^{-1}(x)\) does not exist
- D \(f^{-1}(x)=\frac{1}{x}\)
Answer & Solution
Correct Answer
(C) the function \(f^{-1}(x)\) does not exist
Step-by-step Solution
Detailed explanation
We have, \(f(x)=|x|\)
\[
f(x)= \begin{cases}x, & \text { if } x \geq 0 \\ -x, & \text { if } x \leq 0\end{cases}
\]
So, the function \(f^{-1}(x)\) does not exist.
\[
f(x)= \begin{cases}x, & \text { if } x \geq 0 \\ -x, & \text { if } x \leq 0\end{cases}
\]
So, the function \(f^{-1}(x)\) does not exist.
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