What is the Inverse Function of g(x)?

[andydan1056]

Consider the function g(x) represented by the table below:
x -6 -4 -2 0 2 4 6
g(x) -4 -2 4 0 6 -6 2

Complete the table of values for the INVERSE, g^{-1}(x), in the table below:
x -6 -4 -2 0 2 4 6
g^{-1}(x)

 

[ehild]

Consider the function g(x) represented by the table below:
x -6 -4 -2 0 2 4, 6
g(x) -4 -2 4 0 6 -6 2

Complete the table of values for the INVERSE, g^{-1}(x), in the table below:
x -6 -4 -2 0 2 4 6
g^{-1}(x)

Think of of the definition of the inverse function. If g assigns the value y to x, then g^-1 assigns x to y. g^-1g(x)=x.

If g(x) = -6 , x was equal to 4. So g^-1(-6)=g^-1(g(4))=4

Can you continue?

 

[HallsofIvy]

Another way of thinking about it: g is defined by
-6 --> -4
-5 --> -2
-2 --> 4
0 --> 0
2 --> 6
4 --> -6
6 --> 2

The inverse function, g^-1, by definition, reverses that.