Question

Which of the statement is ALWAYS true?

A The inverse of a linear function is a function.
B The inverse of a quadratic function is a function.
C The inverse of a cubic function is a function.
D The inverse of a logarithmic function is a function.

Answer 1

Answer: A. (The inverse of a quadratic function is not a function)

Since a parabola (quadratic function) does not pass the horizontal line test, it is not possible for a quadratic equation to will have an inverse that is also a function.

Option B is wrong because the inverse of a linear function is not always a function because when the linear function has slope, the inverse cannot be a function.

Option C is wrong because the inverse of a quadratic function is never a function because a quadratic function does not pass the horizontal line test

Option D is wrong because the inverse of a linear function is a function, provided that the linear function has no slope.

Explanation: