# Thread: Taking the inverse of a function

1. ## Taking the inverse of a function

So I forget how to find the inverse of a function.
The function I have is f(x) = 3x^2 - x .
I remember that I have to switch the x and y points so that it looks like this
x = 3y^2 - y but I'm not sure how to solve it.
Thanks

2. Originally Posted by the-G
So I forget how to find the inverse of a function.
The function I have is f(x) = 3x^2 - x .
I remember that I have to switch the x and y points so that it looks like this
x = 3y^2 - y but I'm not sure how to solve it.
Thanks
You need to complete the square. First take $\frac{x}{3} = y^2 - \frac{y}{3}$ and then add $\frac{1}{36}$ to both sides of the equation to get $\frac{x}{3} + \frac{1}{36} = y^2 - \frac{y}{3} + \frac{1}{36}$.

Then we have completed the square:

$\frac{x}{3} + \frac{1}{36} = (y - \frac{1}{6})^2$.

Can you finish it from there?