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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:

Liam is looking for an inverse to π ( π₯ ) = β 2 β ( π₯ β 4 ) 2 . He starts with the parabola π¦ = β 2 β ( π₯ β 4 ) 2 . He then reflects this in the line π¦ = π₯ to get the shown parabola π₯ = β 2 β ( π¦ β 4 ) 2 .

Complete Liamβs work by determining the inverse π β 1 whose graph is the given solid curve.

Q2:

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 .

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

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 .

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