SOLUTION: Find the Inverse of the function f(x)= 2/3x -3/5. I know the answer is f-1(x)= -6-x ----- 3 I only ne

Question 80375This question is from textbook Algebra for college students
: Find the Inverse of the function f(x)= 2/3x -3/5.
I know the answer is f-1(x)= -6-x
-----
3

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

Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Given:
.

.
Note that I presume you meant and not which is what you wrote
if the rules of algebraic convention are followed.
.
There are four steps to finding an inverse of the function. These steps are:
.
1. Replace f(x) with y
2. Then replace y by x and also change x to y
3. Solve for y
4. Finally replace y by
.
Let's do it by following these 4 steps. Start with the given:
.

.
Replace f(x) by y to get:
.

.
Step 1 is done. Next do step 2 by changing y to x and also changing x to y. When you
do that the equation from step 1 becomes:
.

.
Step 2 is now done. On to step 3 which tells you to solve for this equation for y.
You can isolate the term that contains y. Do that by adding to both sides of
the equation to get:
.

.
Notice that the terms and cancel each other on the right side so
the equation is reduced to:
.

.
You can get rid of the denominator 5 on the right side by multiplying all the terms on
both sides of this equation by 5. Multiplying everything by 5 results in:
.

.
Now get rid of the denominator of 3 on the right side by multiplying everything on both
sides by 3 to get:
.

.
Now solve for y by dividing both sides by 10 and the result is:
.

.
Step 3 is done. Now replace y with and the answer becomes:
.

.
Presuming that I interpreted your problem correctly, this is the answer you were asked to
find. I'm not sure where you got the answer that you did. Even if I interpreted it incorrectly,
the four step process is correct, and you can use this same method to solve any problem with
inverting a function.
.

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