SOLUTION: I trying to find the inverse of a function. I have to solve for y but I don't know how to do this when there is a variable on the top and bottom. x(x-5)= y ----------> y(y-5)=x

Algebra ->  Equations -> SOLUTION: I trying to find the inverse of a function. I have to solve for y but I don't know how to do this when there is a variable on the top and bottom. x(x-5)= y ----------> y(y-5)=x      Log On


   

Question 157496: I trying to find the inverse of a function. I have to solve for y but I don't know how to do this when there is a variable on the top and bottom.
x(x-5)= y ----------> y(y-5)=x ???
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll start where you left off

y%28y-5%29=x Start with the given equation


y%5E2-5y=x Distribute


y%5E2-5y-x=0 Subtract "x" from both sides


Notice how we have a quadratic equation in the form of ay%5E2%2Bby%2Bc where a=1, b=-5, and c=-x. So to solve for y, we must use the quadratic formula y+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+


y+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ Start with the quadratic formula


Plug in a=1, b=-5, and c=-x



y+=+%285+%2B-+sqrt%28+25%2B4x+%29%29%2F%282%29+ Multiply and simplify


y+=+%285+%2B+sqrt%28+25%2B4x+%29%29%2F%282%29+ or y+=+%285+-+sqrt%28+25%2B4x+%29%29%2F%282%29+ Break up the "plus/minus"


So the inverse of x%28x-5%29=+y is y+=+%285+%2B+sqrt%28+25%2B4x+%29%29%2F%282%29+ or y+=+%285+-+sqrt%28+25%2B4x+%29%29%2F%282%29+


Note: the inverse of x%28x-5%29=+y is NOT a function.