A. If $f$ is an invertible function such that $f ( 3 ) = 3$, then $f ^ { - 1 } ( 3 ) = \frac { 1 } { 3 }$.
B. A one-to-one function is invertible.
C. If $f$ and $g$ are inverses of each other then $f$ and $g$ have the same domain.
A)A and B are true.
B)B and C are true.
C) Only B is true.
D) None of these

Question

Quizplus · Accepted Answer

B. A one-to-one function is indeed invertible because for every output there is exactly one input, making it possible to reverse the function. A and C are incorrect because A assumes a specific relationship between $f(3)$ and $f^{-1}(3)$ without justification, and C is incorrect because $f$ and $g$ having inverses of each other means $f$'s domain is $g$'s range and vice versa, not necessarily that they share the same domain.

A If fff Is an Invertible Function Such That f(3)=3f ( 3 ) = 3f(3)=3

A If $f$ Is an Invertible Function Such That $f ( 3 ) = 3$