Given the function f(x) = 9x+7, find it's inverse

Question

answer choices are:

1. f-1(x) = (x-9)/7

2. f-1(x) = x/9-7

3. f-1(x) = (x-7)/9

4. f-1(x) = x/7-9

Answer 1

Let y = 9x + 7, then

9x = y - 7

x = (1/9)(y - 7)

Now the above is just a function giving the relationship between two variables. The one on the right is the independent variable (you can give it whatever value you want). Call it iv.

The one on the left is the dependent variable (its value depends on the value you give to the independent variable). Call this one dv. Then ...

dv = (1/9)(iv - 7)

or, y = (1/9)(x - 7)

i.e. f^(-1)(x) = (x - 7)/9