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NC.M3.F-BF.4b

Determine if an inverse function exists by analyzing tables, graphs, and equations.

Example Problems

The following table shows a few inputs and outputs of

h(x)

x	h(x)
0	-8
9	-6
19	-1
28	4
37	9
47	13

What is the value of

h^{-1}(9)

The following table shows a few inputs and outputs of r(x).

x	-30	-20	-10	-2	7	17
r(x)	-10	-12	-6	-20	1	-1

What is the value of

r^{-1}(-20)

The following table shows a few inputs and outputs of

z(x)

x	z(x)
-22	-30
-16	-22
-11	-17
-5	-9
0	-2
6	4

What is the value of

z^{-1}(-9)

Khan Academy Resources

Intro to inverse functions Verifying inverse functions by composition Intro to invertible functions Evaluate function expressions Verify inverse functions Evaluate functions from their graph Function rules from equations Function inputs & outputs: graph Restrict domains of functions to make them invertible Evaluate inverse functions Identifying values in the domain Function inputs & outputs: equation Determine if a function is invertible Find inverses of rational functions Finding inverses of linear functions Intro to inverse functions Finding inverse functions: linear Worked example: matching an input to a function's output (equation)Graphing the inverse of a linear function Verifying inverse functions by composition Worked example: two inputs with the same output (graph)Finding inverses of rational functions Restricting domains of functions to make them invertible Evaluating discrete functions Worked example: matching an input to a function's output (graph)Determining if a function is invertible Determining whether values are in domain of function Inputs & outputs of inverse functions Verifying inverse functions from tables Verifying inverse functions by composition: not inverse

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