Relations And Functions Practice Questions Ques22
Question: For which of the following functions is $f^{-1}(f(x)) = x$ always true?
Options:
(A) $f(x) = x^2, x \in \mathbb{R}$
(B) $f(x) = |x| , x \in \mathbb{R}$
(C) $f(x) = e^x, x \in \mathbb{R}$
(D) $f(x) = x + 5, x \in \mathbb{R}$
Show Answer
Answer: D
Explanation:
(A) Incorrect. $f(x) = x^2$ is not invertible for all real numbers.
(B) Incorrect. $f(x) = |x|$ is not invertible for all real numbers.
(C) Incorrect. While $e^x$ is invertible, its inverse is $\ln(x)$, which is only defined for positive real numbers.
(D) Correct. $f(x) = x + 5$ is a one-to-one function and is invertible for all real numbers.
BETA
