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8-12.
  1. A table can be used as a useful tool for finding some inverse functions. When the function has only one x in it, the function can be described with a sequence of operations, each applied to the previous result. Consider the following table for f(x) = 2 + 3. Homework Help ✎

    1st

    2nd

    3rd

    4th

    What f does to x:

    subtracts 1

    multiplies by 2

    adds 3


    Since the inverse must undo these operations, in the opposite order, the table for f −1(x) would look like the one below.

    1st

    2nd

    3rd

    4th

    What f−1 does to x:

    subtracts 3

    divides by 2

    ( )2

    adds 1

    1. Copy and complete the following table for g1(x) if g(x) = (x + 1)2 − 2 for x ≥ –1.

      1st

      2nd

      3rd

      4th

      What g does to x:

      adds 1

      ( )2

      divides by 3

      subtracts 2

      What g−1 does to x:

    2. Write the equations for f −1(x) and g1(x).

1st: adds 2
2nd: multiplies by 3
4th: subtracts 1

What is the correct domain for this inverse function?