AP®MathsCollege BoardPrecalculusExam QuestionsExponential & Logarithmic FunctionsComposite & Inverse Functions

Composite & Inverse Functions (College Board AP® Precalculus): Exam Questions

11 mins6 questions

Select a download format for Composite & Inverse Functions

Scroll for more

Select an answer set to view for
Composite & Inverse Functions

1
Sme Calculator
2 marks

The function space f is decreasing and is defined for all real numbers. The table gives values for space f open parentheses x close parentheses at selected values of x.

space x

-2

-1

0

1

2

space f open parentheses x close parentheses

14

7

3.5

1.75

0.875

The function g is given by g open parentheses x close parentheses equals negative 0.167 x cubed plus x squared minus 1.834.

(i) The function h is defined by h open parentheses x close parentheses equals open parentheses g ring operator f close parentheses open parentheses x close parentheses equals g open parentheses f open parentheses x close parentheses close parentheses. Find the value of h open parentheses 1 close parentheses as a decimal approximation, or indicate that it is not defined. Show the work that leads to your answer.

(ii) Find the value of space f to the power of negative 1 end exponent open parentheses 3.5 close parentheses, or indicate that it is not defined.

How did you do?

2a
Sme Calculator
2 marks
Graph of a function on a grid, with a curve starting at x=-3.5 and ending at x=3.5. From the start, it dips down, then turns back up, and then dips down again before getting to x=3.5. The points (-3, 1), (0, 1) and (3, 1) are on the curve.

The figure shows the graph of the function space f on its domain of negative 3.5 less or equal than x less or equal than 3.5. The points left parenthesis negative 3 comma space 1 right parenthesis, left parenthesis 0 comma space 1 right parenthesis, and left parenthesis 3 comma space 1 right parenthesis are on the graph of space f. The function g is given by g open parentheses x close parentheses equals 2.916 times open parentheses 0.7 close parentheses to the power of x.

(i) The function h is defined by h open parentheses x close parentheses equals open parentheses g ring operator f close parentheses open parentheses x close parentheses equals g open parentheses f open parentheses x close parentheses close parentheses. Find the value of h open parentheses 3 close parentheses as a decimal approximation, or indicate that it is not defined.

(ii) Find all values of x for which space f open parentheses x close parentheses equals 1, or indicate that there are no such values.

How did you do?

2b
2 marks

(i) Determine if space f has an inverse function.

(ii) Give a reason for your answer based on the definition of a function and the graph of y equals f open parentheses x close parentheses.

How did you do?

3
Sme Calculator
2 marks

The function f is increasing and is defined for x greater than 0. The table gives values of f open parentheses x close parentheses at selected values of x.

x

1

2

4

8

16

f open parentheses x close parentheses

3

5

7

9

11

The function g is given by g open parentheses x close parentheses equals negative 0.1371 x to the power of 4 plus x cubed minus 1.2 x squared.

(i) The function h is defined by h open parentheses x close parentheses equals open parentheses g ring operator f close parentheses open parentheses x close parentheses equals g open parentheses f open parentheses x close parentheses close parentheses. Find the value of h open parentheses 2 close parentheses as a decimal approximation, or indicate that it is not defined. Show the work that leads to your answer.

(ii) Find the value of f to the power of negative 1 end exponent open parentheses 7 close parentheses, or indicate that it is not defined.

How did you do?