Every function has an inverse relation. If this inverse relation is also a function, then it is called an inverse function. In other words, the inverse of a function f is another function such that they undo each other.
|Definition of First Function||Substitute Second Function||Simplify|
Some of the coordinates of the function g are shown in the table. Find then graph g and on the same coordinate plane.
An inverse of a function reverses its x- and y-coordinates. When a function is expressed as a table of values, finding its inverse means switching the coordinates. For example, the point (-4,3) on g becomes (3,-4) on The following table describes
We can graph both g and by marking the points from both tables on the same coordinate plane.
Just as f(x)=y shows the input-output relationship of f, so does Thus, replacing y with gives the rule for the inverse of f.
Notice that in f, the input is multiplied by 2, decreased by 1 and divided by 3. From the rule of it can be seen that x undergoes the inverse of these operation in the reverse order. Specifically, x is multiplied by 3, increased by 1, and divided by 2.
Consider the quadratic function f(x)=3x2. Find its inverse function for when x>0.