IB Maths Inverse Functions Explanation

Question

In an example question in my textbook that asks for the inverse of f(x) = 4 - 3x the answer goes as follows:

 

y=4-3x

x=4-3y

x-4=-3y

x-f/-3 = y

y=4-x/3

 

I do not understand how x-f/-3 = y can be changed to y=4-x/3.

What is the rule behind this?

Answer 1

The "x-f" should be x-4.  The correct sequence is:

 

y = 4 - 3x

 

Switch the x's and y's:

 

x = 4 - 3y

 

Solve for y:

 

x-4 = -3y

 

(x-4)/(-3) = y

 

Here you are dividing by a negative number, -3, so multiply by (-1)/(-1).  That changes the (x-4) to (4-x) and the -3 to 3.

 

(4-x)/3 = y = f^-1(x)