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Cogito

AP Precalculus · Chapter 4 · Lesson 2

Practice Worksheet

Inverse Functions

Undoing, and when it is allowed.

11 problems · about 22 minutes · AP Precalculus 1.15

NameDate

Figure — use these to answer the problems

The square root is the inverse of squaring, once the domain is restricted.
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y = 1√x + 0
a1
Figure 1

Warm Up

Straightforward practice. Get the method working first.

4 problems

  1. f(x) = 4x + 2. Inverse of 22?

    Answer

  2. f(x) = x − 4. Inverse of 10?

    Answer

  3. f(x) = 2x. Inverse of 18?

    Answer

  4. f(x) = 3x − 1. Inverse of 14?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. Select every function that has an inverse over all real numbers.

    • f(x) = 2x + 1
    • f(x) = x²
    • f(x) = x³
    • f(x) = |x|
    • Tick every box that applies.

  2. Across which line is an inverse a reflection? Answer 1 for y = x, 2 for the x-axis.

    Answer

  3. The point (3, 11) is on f. What is the x of the matching point on the inverse?

    Answer

Stretch Yourself

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

4 problems

  1. Order the steps for finding an inverse.

    Write 1 to 4 in the boxes to put these in order.

    • Write y = f(x)
    • Swap x and y
    • Solve for y
    • Check with one point

  2. Why has x² no inverse over all reals? Answer 1 if two inputs share an output, 0 otherwise.

    Answer

  3. Undoing

    f(x) = x + 8. What does the inverse give when the input is 20?

    Answer

  4. The Round Trip

    f(x) = 5x. What is f applied to the inverse of 45?

    Answer