# Thread: How to solve inverse function?

1. ## How to solve inverse function?

Find a formula f-1(x). Give the domain of f-1, including any restrictions "inherited" from f
So one of my problem is f(x)=3x-6

But I'm kind of confused on how to start off
At first I thought it was like having the equation all go to the power of -1
So I got y=(1/3)x-(1/6)

But in the answer book it says: y=(1/3)x + 2

2. ## Re: How to solve inverse function?

Originally Posted by Chaim
Find a formula f-1(x). Give the domain of f-1, including any restrictions "inherited" from f
So one of my problem is f(x)=3x-6, answer book it says: y=(1/3)x + 2
Start with $\displaystyle x=3y-6$. Solve for $\displaystyle y$.

3. ## Re: How to solve inverse function?

Originally Posted by Plato
Start with $\displaystyle x=3y-6$. Solve for $\displaystyle y$.
x = 3y - 6
x - 6 = 3y
(x/3) - 2 = y

Oh!
Now I see!
Thanks!
So that means the inverse really means solving for 'y' when you have 'x' as a single

4. ## Re: How to solve inverse function?

Originally Posted by Chaim
x = 3y - 6
x - 6 = 3y
(x/3) - 2 = y

Oh!
Now I see!
Thanks!
So that means the inverse really means solving for 'y' when you have 'x' as a single
Finding the inverse function (not the "reciprocal" which is 1/f) for any function means swapping x and y and then solving for y. It is, strictly speaking, the swapping of x to y that gives the inverse function but we always want a function written in the form y= f(x) so we always want to solve for y.

5. ## Re: How to solve inverse function?

Originally Posted by HallsofIvy
Finding the inverse function (not the "reciprocal" which is 1/f) for any function means swapping x and y and then solving for y. It is, strictly speaking, the swapping of x to y that gives the inverse function but we always want a function written in the form y= f(x) so we always want to solve for y.
Oh!
Ok thanks!