
Functions and Graphs 2-11
Figure 2.4
x
y
x = y
2
y = x
2
Example 2.9 Find the inverse of the function f(x) = x
1/3
+ 2.
Solution: f is one-to-one, and hence does have an inverse. Here is a two-step method to find the
inverse:
Write y = f(x) and solve for x. Here, y = x
1/3
+ 2 gives:
x
1/3
= y - 2.
Hence, x = (y - 2)
3
.
Switch x and y in the resulting equations. The resulting functions of x are the inverse.
Switching x and y gives y = (x - 2)
3
.
Thus, the inverse function is f
-1
(x) = (x - 2)
3
.
Example 2.10 Find the inverse of the function f defined by f(x) = log(x + 2) - 3.
Solution: f is one-to-one, and hence does have an inverse.
Write ...