### Home > CCA2 > Chapter 8 > Lesson 8.1.1 > Problem 8-12

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 ✎ 1

^{st}2

^{nd}3

^{rd}4

^{th}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.1

^{st}2

^{nd}3

^{rd}4

^{th}What

*f*^{−1}does to*x*:subtracts 3

divides by 2

( )

^{2}adds 1

Copy and complete the following table for

*g*^{−}^{1}(*x*) if*g*(*x*) =( *x*+ 1)^{2}− 2 for*x*≥ –1.1

^{st}2

^{nd}3

^{rd}4

^{th}What

*g*does to*x*:adds 1

( )

^{2}divides by 3

subtracts 2

What

*g*^{−1}does to*x*:Write the equations for

*f*^{ −1}(*x*) and*g*^{−}^{1}(*x*).

1st: adds 2

2nd: multiplies by 3

4th: subtracts 1

What is the correct domain for this inverse function?