SOLUTION: find the inverse of following functions: (a) f(x)=(x^3 + 5)/(x-3) , x≠3 (b)f(x)=(x^3 - 8)/(x^2

SOLUTION: find the inverse of following functions: (a) f(x)=(x^3 + 5)/(x-3) , x≠3 (b)f(x)=(x^3 - 8)/(x^2 - 4) , x≠�2

Question 346009: find the inverse of following functions:
(a) f(x)=(x^3 + 5)/(x-3) , x≠3

(b)f(x)=(x^3 - 8)/(x^2 - 4) , x≠�2
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
To find inverses:

Replace the function notation, if any, with a "y".
Rewrite the equation writing an "x" where you have a "y" and writing a "y" where you have a "x". This step is where you are changing the function to its inverse.
If possible, solve the resulting equation for y. If you are able to find a single expression for y, then the inverse of the function is a function, too.

Let's try this out:

1) Replace function notation:

2) Swap the x's and y's:

This is the inverse relation.
3) Solve fo y, if possible.
Multiply both sides by y-3:

Gather the y terms on one side and everything else on the other side of the equation. I'm going to subtract xy and 5 from each side:

At this point I don't see a way to solve for y. So the inverse is not a function.

1) Replace function notation:

2) Swap the x's and y's:

This is the inverse relation.
3) Solve for y, if possible
Multiply both sides by

Gather the y terms on one side:

And again I don't see a way to solve for y. So this inverse in not a finction either.
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