College Algebra & Trigonometry, 2018a

4.8. INVERSE FUNCTIONS 229
4.8 Inverse Functions
An inverse function undoes the action of the original function. So the inverse of a
function that squared a number would be a function that square rooted a number.
In general, an inverse function will take a y value from the original function and
return the x value that produced it.
We can see this in an application. Given an object with little or no air resistance
that is dropped from 100 ft., the function that describes its height as a function of
time would be:
H(t) = 100 − 16t 2
In this function, H(t) is the height of the object at time t. If we wanted to turn this
around so that it described the time for a given height, then we would want to
isolate the t variable. In this example, the graph of the function would change in
that the original independent variable - t, becomes the dependent variable in the
inverse function.
h = 100 − 16t 2
16t 2 = 100 − h
t 2 = 100 − h
16
t =
√
100 − h
16
T (h) =
√
100 − h
4