f -1(x) = 4x
If you supply 3 for the function of F so f(3) = 4x then 4 x 3 = 12
The inverse would be
One way to work out an inverse function is to reverse the operations that f carries out on a
number. Here is a simple example. We shall set f(x) = 4x, so that f takes a number x and
multiplies it by 4:
f(x) = 4x (multiply by 4).
We want to define a function that will take 4 times x, and send it back to x. This is the same
as saying that f
−1
(x) divides x by 4. So
f
−1
(x) = 1
4
x (divide by 4).
There is an important point about notation here. You should notice that f
−1
(x) does not mean
1/f(x). For this example, 1/f(x) would be 1/4x with the x in the denominator, and that is not
the same as 1
4
x.
