# 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 $y = f^{-1}(x)$ where $x = y^2 - y$.

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 $y=x^2-x$ 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?

5. Originally Posted by algebra2
mr. fantastic, i'm doing the same question, but if you graph $y=x^2-x$ 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?
It means that it doesn't have an inverse function. However, an inverse relation exists.

If you want an inverse function, then the domain of f needs to be restricted so that f is a 1-to-1 function. The question doesn't say what the domain is ....