Question

What is the inverse function of F(x) = -3/2x - 8

Answer 1

f-1(x)=-
`(2)/(3)`x-
`(16)/(3)`

Explanation:

First, switch f(x) to the variable "y".

y=-
`(3)/(2)`x-8

Next, swap "x" and "y" with each other.

x=-
`(3)/(2)`y-8

Next, lets move the denominator of 2 to the other side by multiplying both sides by 2. Your result will be...

2x=-3y-16

Now move -16 to the left side.

16+2x=-3y

To get "y" by itself, lets divide each side by -3. Our result is...

y=-
`(2)/(3)`x-
`(16)/(3)`

To finish the problem off, replace y with f-1(x) and your complete answer will be...

f-1(x)=-
`(2)/(3)`x-
`(16)/(3)`