AP®MathsCollege BoardPrecalculusExam QuestionsExponential & Logarithmic FunctionsComposite & Inverse Functions

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

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Composite & Inverse Functions

1
Sme Calculator
1 mark

The function f is given by f \left(x\right) = x^{2} - 2, and the function g is given by g \left(x\right) = \frac{x + 1}{x}. Which of the following is an expression for f \left(g \left(x\right)\right) ?

  • fraction numerator x squared minus 1 over denominator x squared minus 2 end fraction

  • \frac{- x^{2} + 2 x + 1}{x^{2}}

  • \frac{- x^{2} + 1}{x^{2}}

  • \frac{x^{2} + 2 x - 1}{x^{2}}

Choose your answer

2
Sme Calculator
1 mark

The table gives values for the functions f and g at selected values of x. Functions f and g are defined for all real numbers. Let h be the function defined by h \left(x\right) = f \left(g \left(x\right)\right). What is the value of h \left(1\right) ?

x

- 2

- 1

0

1

2

f \left(x\right)

3

- 1

2

0

- 2

g \left(x\right)

1

2

- 1

- 2

0

  • 3

  • 0

  • - 2

  • - 1

Choose your answer

3
1 mark

The graph of the piecewise-linear function f is shown in the figure. Let g be the inverse function of f. What is the maximum value of g ?

Graph of a piecewise-linear function f consisting of two line segments: from (2, 3) to (5, 6), and from (5, 6) to (8, 14).

  • \frac{1}{14}

  • \frac{1}{8}

  • 8

  • 14

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