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Lesson: Using a Graph to Find an Inverse

In this lesson, explore and understand the symmetry between the graph of a function and the graph of its inverse, and learn how to use a graph to find the inverse of a function.

Worksheet: Using a Graph to Find an Inverse • 7 Questions

Q1:

The following is the graph of .

Which one is the graph of the inverse function ?

A(a)
B(c)
C(b)

Q2:

Christopher is looking for an inverse to . He starts with the parabola . He then reflects this in the line to get the shown parabola .

Complete Christopher’s work by determining the inverse whose graph is the given solid curve.

Q3:

Consider the two following figures.

The first figure shows the graph of and a tangent to the graph with gradient 1. This tangent meets the graph at a point with -coordinate .

The second figure shows the graphs of and its inverse . The graphs cross in the third quadrant and touch in the first quadrant.

What is the value of ?

What are the -coordinates of the two points of intersection of the graphs in the second figure?

A and
B and
C and
D and
E and

Q4:

The graphs of and its inverse intersect at three points, one of which is .

Determine the value of .

Find the -coordinate of the point marked on the figure.

Q5:

The following graph is of the function , with its maximum at , minimum at , and zero at marked.

Find an expression for the inverse function when is restricted to the interval .

What is the domain of in this case?

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