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Cogito

Integrated Math 3 · Chapter 3 · Lesson 3

Practice Worksheet

Inverse Functions

Undoing a function, when it can be undone.

12 problems · about 22 minutes · F-BF.B.4

NameDate

Figure — use these to answer the problems

Set the slope to 1 and the intercept to 0 to draw y = x, the line every inverse reflects across.
-10-10-5-5551010
y = x
Slope1
y-intercept0
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. f(x) = 2x + 3. What is f⁻¹(9)?

    Answer

  2. Why must a function be one-to-one to have an inverse?

    • Otherwise one output would have to map back to two inputs.
    • Otherwise its graph would be curved.

  3. f(x) = x + 5. What is f⁻¹(12)?

    Answer

  4. f(x) = 4x. What is f⁻¹(20)?

    Answer

  5. f(x) = x³. What is f⁻¹(27)?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. f(x) = x² on x ≥ 0. What is f⁻¹(49)?

    Answer

  2. f(f⁻¹(9)) equals what?

    Answer

  3. The range of f is y ≥ 4. Smallest value in the domain of f⁻¹?

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. Which functions are one-to-one over all real numbers?

    • f(x) = 3x minus 7
    • f(x) = x cubed plus 1
    • f(x) = x to the fourth
    • f(x) = the absolute value of x
    • Tick every box that applies.

  2. f(x) = (x − 1) ÷ 4. What is f⁻¹(2)?

    Answer

  3. The Inverse

    f(x) = 3x + 6. What is f⁻¹(12)?

    Answer

  4. The Point

    The point (3, 8) lies on f. What is f⁻¹(8)?

    Answer