7
QuizMultiple Choice

Function Inverses

Question 7 • 26/27 ALGEBRA II A

Which statement could be used to explain why f(x) = 2x – 3 has an inverse relation that is a function?

Answer
A
The graph of f(x) passes the vertical line test.
B
f(x) is a one-to-one function.
C
The graph of the inverse of f(x) passes the horizontal line test.
D
f(x) is not a function.

Explanation

A function has an inverse that is also a function when the original function is one-to-one. For f(x) = 2x − 3, different x-values produce different outputs because its slope is nonzero, so f is one-to-one. Therefore, choice B, “f(x) is a one-to-one function,” explains why its inverse relation is a function.

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