We begin with the definition: Inverse Functions – The functions f(x) and g(x) are inverses if both
Verify that the given functions are inverses.
Determine whether or not the given functions are inverses.
Take the time to review one-to-one (1-1) functions because it turns out that if a function is 1-1 then it has an inverse. Therefore, we may think of the horizontal line test as a test that determines if a function has an inverse or not.
Next we outline a procedure for actually finding inverse functions.
Step 1: Replace f(x) with y.
Step 2: Interchange x and y.
Step 3: Solve the resulting equation for y.
Step 4: Replace y with the notation for the inverse of f.
Step 5: (Optional) Verify that the functions are inverses.
Find the inverse of the given function.
Symmetry of Inverse Functions – If (a, b) is a point on the graph of a function f then (b, a) is a point on the graph of its inverse. Furthermore, the two graphs will be symmetric about the line y = x.
In the following graph, see that the functions
Given the graph of a 1-1 function, graph its inverse and the line of symmetry.
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