(1) A formal algebraic process for finding the inverse of a function: switch x and y and solve for the new y:
The inverse is .
(2) A different way to find an inverse, if the function is relatively simple:
Since an inverse function "un-does" what the function does, determine what operations were performed on the input by the original function; the inverse function will perform the inverse operations in the opposite order.
For this example, the operations performed on the input by the original function are
(1) subtract 7
(2) take log base 10
The inverse operations, in the opposite order, are
(1) raise 10 to the power
(2) add 7
