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In this lesson, we will learn how to use compositions of functions to find and justify inverses of functions.

Q1:

Determine and so that is an inverse function to by considering .

Q2:

Let π ( π₯ ) = 2 π₯ β 1 3 π₯ β 2 . Solve π¦ = π ( π₯ ) to find an expression for π ( π₯ ) β 1 .

Find π ( π₯ ) β 1 and π ( π₯ ) β 1 when π ( π₯ ) = 5 π₯ + 2 2 π₯ β 5 and π ( π₯ ) = 5 π₯ + 2 2 π₯ + 1 .

Let π ( π₯ ) = π π₯ + π π π₯ + π and π ( π₯ ) = π π₯ β π β π π₯ + π . By considering the simplification of π ( π ( π₯ ) ) , what, if any, is the relation between π and π ?

Let π ( π₯ ) = 2 π₯ + 1 3 π₯ β 2 , π ( π₯ ) = β 2 π₯ β 1 β 3 π₯ + 2 , π ( π₯ ) = 4 π₯ + 2 6 π₯ β 4 1 2 a n d . By considering the simplifications of π β π 1 and π β π 2 , what, if any, are the relations between these functions?

Suppose that π = π β 1 , where π ( π₯ ) = π π₯ + π π π₯ + π . What must be true of π , π , π , and π ?

Q3:

Which of the following is a necessary condition for a function π to be invertible?

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