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Question: Answered & Verified by Expert
If $f: R \rightarrow R$ is defined by $f(x)=|x|$, then
MathematicsFunctionsCOMEDKCOMEDK 2020
Options:
  • A $f^{-1}(x)=\frac{1}{|x|}$
  • B $f^{-1}(x)=-x$
  • C $f^{-1}(x)=\frac{1}{x}$
  • D The function $f^{-1}(x)$ does not exist.
Solution:
1033 Upvotes Verified Answer
The correct answer is: The function $f^{-1}(x)$ does not exist.
Since, $f(x)=|x|$ is neither one-one nor onto, 30 $f(x)$ is not invertible.
$\therefore f^{-1}(x)$ does not exist.

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