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  1. Which of the following is true of functions and their inverses?
AThe inverse of a quadratic function is not a function.
BThe inverse of a linear function is always a function.
CThe inverse of a quadratic function is always a function.
DThe inverse of a linear function is not a function.

Verified Answer :

W0lf93

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.

The correct answer is:


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


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.

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