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

Graphing Inverse Functions Example 1: Graph the function and it’s inverse. Then find the equation of the inverse function. f(x)=x3-1 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.