1. Algebra 2/Trig Name:__________________________
7.4 Inverse Functions Date: _______________ Block:______
If you interchange all of the x-coordinates and y-coordinates you will create the ___________
Given a function f(x), it's ____________ function is denoted _______.
f(x) = {(1,5),(2,6), (3,7), (4,8)}
f-1(x) = {(__,__),(__,__),(__,__),(__,__)}
Notice that the _________ of the original function is now the ___________of the inverse function. Similarly, the _________ of the original function is now the ____________of the inverse function.
Finding the Inverse of a Function Algebraically
We verify by taking the composition of the function and it’s inverse. You will always get the identity function h(x)=______
Example 1: f(x)=______________
(f◦f-1)(x)=x
f(x) = -7x+5
f-1(x)=
Example 2 - Find f-1(x) and verify that it is the inverse function
Example 3 - Find g-1(x) and verify that it is the inverse function

2. Graphing Inverse Functions
Example 1: Graph the function and it’s inverse. Then find the equation of the inverse function.
f(x)=x f-1(x)=_______
f(x)
Domain:__________
Range:___________
f-1(x)
Range:__________
Remember - given a function and its inverse, the Domain and Range should be ___________!
Given the graph of a function, you could draw the graph of its inverse function by reflecting it across the line y = ___.
g(x)
Domain:__________
Range:___________
g-1(x)
Range:__________
g(x)
Not all functions have inverses that are also FUNCTIONS...
Notice – for each point (__,__) on the original graph, f(x), a reflected point (__,__) is on the inverse function, f-1(x), graph.
f(x)=x2-4
You can determine whether a function will have an inverse function by using the ___________________test.
If you can draw a ______________________
anywhere on the graph and only intersect the function at one point, the function will have an _________ function.
This function will/will not have an inverse function.
This function will/will not have an inverse function.