# Thread: Inverse of a Function

1. ## Inverse of a Function

I'm looking to find the inverse function of f(n)= x^2 - x

the fact that x is raised to the power is confusing me.

thanks in advance for some help!

2. change all ys to xs and all xs to ys...and re-arrange to get a new function in terms of your new y...

y= x^2 - 2
x= y^2 - 2
x+2 = y^2
y= sqrt(x+2)

oh and don't forget +/- cos its sqrt

3. Originally Posted by dlee426
I'm looking to find the inverse function of f(n)= x^2 - x

the fact that x is raised to the power is confusing me.

thanks in advance for some help!
The inverse is given by $\displaystyle y = f^{-1}(x)$ where $\displaystyle x = y^2 - y$.

Your job now is to make y the subject. You have several options:

Option 1: First complete the square.

Option 2: Solve for y using the quadratic formula.

Originally Posted by shabz
change all ys to xs and all xs to ys...and re-arrange to get a new function in terms of your new y...

y= x^2 - 2
x= y^2 - 2
x+2 = y^2
y= sqrt(x+2)

oh and don't forget +/- cos its sqrt

4. mr. fantastic, i'm doing the same question, but if you graph $\displaystyle y=x^2-x$ and use the horizontal line test, it doesn't pass and therefore is not one-to-one....so does that mean it doesn't have an inverse?
mr. fantastic, i'm doing the same question, but if you graph $\displaystyle y=x^2-x$ and use the horizontal line test, it doesn't pass and therefore is not one-to-one....so does that mean it doesn't have an inverse?