To determine the inverse of f(x), first replace f(x) with y. Then switch x and y and solve for y.
Inverse: f^(-1)(x) = 3(x+3)/2 Result: Yes, the inverse is a function.
Practice makes perfect
We will begin by finding the inverse of f(x). First, we need to replace f(x) with y. From there, we switch x and y and solve for y.
y=2/3 x-3 → x=2/3 y-3The resulting equation will be the inverse of the given function.
Finally, to indicate that this is the inverse function of f(x), we will replace y with f^(- 1)(x).
f^(- 1)(x)=3(x+3)/2
A function is a relation where each input is related to exactly one output. In this case, for each x in f^(- 1)(x), there is only one value of y. Therefore, f^(- 1)(x) is a function.
