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

Q1:

The following is the graph of π ( π₯ ) = 2 π₯ β 1 .

Which one is the graph of the inverse function π ( π₯ ) β 1 ?

Q2:

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

Complete Amirβs work by determining the inverse whose graph is the given solid curve.

Q3:

The following graph is of the function π ( π₯ ) = 6 π₯ + 8 π₯ + 1 2 , with its maximum at οΌ 1 3 , 9 ο , minimum at ( β 3 , β 1 ) , and zero at β 4 3 marked.

Find an expression for the inverse function π β 1 when π is restricted to the interval π₯ β₯ 1 3 .

What is the domain of π β 1 in this case?

Q4:

Consider the two following figures.

The first figure shows the graph of π ( π₯ ) = π₯ ο© and a tangent to the graph with gradient 1. This tangent meets the graph at a point with π₯ -coordinate 1 β 3 .

The second figure shows the graphs of π ( π₯ ) = π₯ + π ο© and its inverse π ( π₯ ) = ( π₯ β π ) ο± ο§ ο ο’ . The graphs cross in the third quadrant and touch in the first quadrant.

What is the value of π ?

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

Q5:

The graphs of π ( π₯ ) = π₯ + π ο© and its inverse π ( π₯ ) ο± ο§ intersect at three points, one of which is οΌ 4 5 , 4 5 ο .

Determine the value of π .

Find the π₯ -coordinate of the point π΄ marked on the figure.

Find the π₯ -coordinate of the point π΅ marked on the figure.

Q6:

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?

Q7:

The following graph is of the function π ( π₯ ) = 6 π₯ + 8 π₯ + 1 2 , with its maximum at οΌ 1 3 , 9 ο , minimum at ( β 3 , β 1 ) , and zero at β 4 3 labeled.

Find an expression for the inverse function π β 1 when π is restricted to the interval β 4 3 < π₯ β€ 1 3 .

Q8:

Determine whether the inverse of the represented function is a function or not.

Q9:

In the given figure, the green points represent the function π ( π₯ ) . Do the blue points represent π ( π₯ ) β 1 ?

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