SOLUTION: Find the inverse of the function f(x)= -3x-6. I know the answer is -6-x

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Question 80380This question is from textbook Algebra for college students
: Find the inverse of the function f(x)= -3x-6. I know the answer is
-6-x
f-1(x)= ------
3

I only need the solution on how it was figured out. This question is from textbook Algebra for college students

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
.
f%28x%29+=+-3x+-+6
.
Find the inverse through the following process.
.
First replace f(x) with y to get:
.
y+=+-3x+-+6
.
Now replace x by y and y by x to get:
.
x+=+-3y+-+6
.
Solve this equation for y just as you would an ordinary equation. This can be done by
first adding 6 to both sides of the equation to eliminate the -6 on the right side to
get:
.
x+%2B+6+=+-3y
.
Then solve for y by dividing both sides by -3
.
%28x+%2B+6%29%2F-3+=+-3y%2F-3
.
Simplifying this results in:
.
-%28x+%2B+6%29%2F3+=+y
.
Transpose sides and the result is:
.
y+=+-%28x%2B6%29%2F3+
.
Apply the negative sign in front of the right side to each of the terms in the numerator
and you get:
.
y+=+%28-x+-+6%29%2F3+
.
Finally replace y by f%5E-1 to get:
.
f%5E-1+=+%28-x-6%29%2F3
.
Other than reversing the order of the two terms in the numerator this is the
answer you
gave in the problem.
.
Hope this helps you understand the four basic steps in finding the inverse of a function:
.
1. Replace f%28x%29 with y
2. Interchange x and y
3. Solve for y in terms of x and
4. Replace y with f%5E-1
.