Question

2. Which of the following is true of functions and their inverses?

A. The inverse of a quadratic function is not a function.
B. The inverse of a linear function is always a function.
C. The inverse of a quadratic function is always a function.
D. The inverse of a linear function is not a function.

Answer 1

The correct answer is:

A) The inverse of a quadratic function is not a function.

Step-by-step explanation:

The inverse of a function is a function if and only if each element of the range (y-coordinates) is mapped to one element of the domain (x-coordinates).

Each y must be mapped to one x; this means no y can be repeated. This means if we draw a horizontal line through any part of the graph of an inverse function, it should not hit more than 1 point.

The graph of a quadratic function is a parabola, or a u-shaped graph. If we draw a horizontal line through a parabola, it will hit twice everywhere except the vertex. This means the inverse of a quadratic function is not itself a function.

Answer 2

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.