The inverse of a function reverses its - coordinates. If, for a function is an input and is its corresponding output, for the inverse, is the input and would be the corresponding output.Some function families are inverses of each other. This is because some functions undo each other. For example, and are inverses because radicals and exponents (with the same index) undo each other.
Some of the coordinates of the function are shown in the table. Find then graph and on the same coordinate plane.
An inverse of a function reverses its - and -coordinates. When a function is expressed as a table of values, finding its inverse means switching the coordinates. For example, the point on becomes on The following table describes
We can graph both and by marking the points from both tables on the same coordinate plane.
To begin, since describes the input-output relationship of the function, replace with in the function rule.
Because the inverse of a function reverses and the variables can be switched. Notice that every other piece in the function rule remains the same.
Just as shows the input-output relationship of so does Thus, replacing with gives the rule for the inverse of
Notice that in the input is multiplied by decreased by and divided by From the rule of it can be seen that undergoes the inverse of these operation in the reverse order. Specifically, is multiplied by increased by and divided by
Consider the quadratic function Find its inverse function for when