Which statement describes how the graph of a function, h(x), and its inverse, h‒1(x), are related?
Answer
A
The line y = ‒x is the perpendicular bisector of each segment connecting a point on h(x) to the corresponding point on h‒1(x).
B
The line y = x is the perpendicular bisector of each segment connecting a point on h(x) to the corresponding point on h‒1(x).
C
The graph of the inverse of h(x) is a reflection over the line y = 0 of the graph of h(x).
D
The y-axis is the perpendicular bisector of each segment connecting a point on h(x) to the corresponding point on h‒1(x).
Explanation
If (a, b) is on the graph of h, then (b, a) is on the graph of its inverse. The segment joining these points has its midpoint on the line y = x, and that line is perpendicular to the segment, so it is the segment’s perpendicular bisector. Thus, the correct statement is that y = x is the perpendicular bisector of each corresponding segment.
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