f(x)= 1/4x - 3/4, Find f^-1(x)

Question

Please explain steps and answer.

Thank you!

Answer 1

We swap x and y and solve for y.

y = 1/4x - 3/4

x = 1/4y - 3/4

x + 3/4 = 1/4y

4x + 3 = y

f^-1(x) = 4x + 3

Answer 2

A function f^-1(x) means that you are looking for the "inverse" of the original function. Essentially, this is a function that would "undo" the other function.

One way to think of this process is to look at the operations in the original equation, and then do the opposite of those operations in reverse order.

In this example, you are:

1. Multiplying by 1/4
2. Subtracting 3/4

So the opposite, in reverse order, would be:

1. Adding 3/4
2. Dividing by 1/4 (or multiplying by 4)

This would give you (x + 3/4) * 4, which simplifies to 4x + 3.