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In this lesson, we will learn how to find the inverse of a function by changing the subject of the formula.

Q1:

Determine the inverse of π ( π₯ ) = 1 3 π₯ + 2 .

Q2:

Find the inverse of the function π ( π₯ ) = 4 π₯ .

Q3:

Find the inverse of the function .

Q4:

Determine the inverse function of π ( π₯ ) = ( π₯ + 6 ) β 5 2 , where π₯ β₯ β 6 .

Q5:

Find the inverse of the function π = { ( 2 , 7 ) , ( β 2 , 4 ) , ( β 6 , 5 ) , ( β 1 0 , 2 ) } .

Q6:

Solve β π₯ β 7 = β 3 .

Q7:

Bassem is trying to find the inverse of . He sets and then finds and then . What does Tom determine to be?

Q8:

Let π ( π₯ ) = 3 π₯ + 5 and π ( π₯ ) = π₯ β 5 3 . Is it true that π is the inverse of π and π is the inverse of π ?

Q9:

Find the inverse of the function π ( π₯ ) = 6 π₯ 3 .

Q10:

What is the inverse of the function π¦ = 7 π₯ β 5 ?

Q11:

Determine the domain on which the function has an inverse.

Q12:

If π β 1 is the inverse function of the function π then which of the following statements is true?

Q13:

Q14:

Find the inverse of the function , where .

Q15:

Find π ( π₯ ) β 1 for π ( π₯ ) = β π₯ + 3 and state the domain.

Q16:

Find π ( π₯ ) β 1 for π ( π₯ ) = 3 + β π₯ 3 .

Q17:

The period π , in seconds, of a simple pendulum as a function of its length π , in feet, is given by π ( π ) = 2 π ο π 3 2 . 2 . Express π as a function of π , and determine the length of a pendulum with a period of 2 seconds.

Q18:

The figure below represents the function π π β π : . Find the value of π ( 4 ) β 1 .

Q19:

For what numbers π can we solve β π₯ β 7 = π ?

Q20:

The solid part of the following graph of π ( π₯ ) = | 3 ( π₯ + 3 ) | shows how we can restrict the domain to obtain an inverse.

What is the domain of the inverse?

What is the range of the inverse?

Give a formula for the inverse.

Q21:

The following tables are partially filled for functions π and π that are inverses of each other. Determine the values of π , π , π , π , and π .

Q22:

A car travels at a constant speed of 50 miles per hour. The distance the car travels in miles is a function of time, π‘ , given in hours by π ( π‘ ) = 5 0 π‘ . Find the inverse function expressing the time of travel in terms of the distance traveled. Find π‘ ( 1 8 0 ) .

Q23:

Use the table to find β ( 3 0 ) β 1 .

Q24:

Does the function π , where π = { ( 5 , 3 ) , ( 9 , 7 ) , ( 1 1 , 1 0 ) } , have an inverse?

Q25:

Which of the following pairs of functions are inverses for all π₯ β β β 0 ?

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