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Home > A2C > Chapter 11 > Lesson 11.3.1 > Problem 11-132

11-132.
  1. For the function, complete parts (a) through (d) below. Homework Help ✎

    1. Sketch the graph and the inverse.

    2. Find the equation of the inverse function.

    3. Determine the domain and range of the inverse.

    4. Compute f −1(f (5)).

First, graph the function. Then, reflect the graph across
y = x.

Replace f(x) with y, then switch the variables.

Now solve for y.

Do not forget to replace y with f − 1(x).

f −1(x) = (2(x + 1))2 − 4

See graph in part (a).

x ≥ −1, y ≥ −4

Substitute 5 for x in the function f(x). Now substitute the answer you found for f(x) for x in the inverse function
f −1(x).

f −1(f(5)) = 5