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.
In this context, the -1 indicates an inverse function not a negative exponent.
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.