SOLUTION: How do i find the inverse function of: f(x) = x^2 - 2x, x>1 I went as far as saying that x^2 - 2x = y but now i have no idea how to solve it:( any kind of help is apprecia

Algebra ->  Functions -> SOLUTION: How do i find the inverse function of: f(x) = x^2 - 2x, x>1 I went as far as saying that x^2 - 2x = y but now i have no idea how to solve it:( any kind of help is apprecia      Log On


   

Question 1163830: How do i find the inverse function of:
f(x) = x^2 - 2x, x>1

I went as far as saying that x^2 - 2x = y but now i have no idea how to solve it:( any kind of help is appreciated!
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
The graph is this half of a parabola.



The inverse is its projection in the identity line whose equation is
y = x, the dotted line below



matrix%281%2C3%2C%0D%0A%22f%28x%29%22+=+x%5E2+-+2x%2C%22%2C%22%2C++x%3E1%29

Change f(x) to y

matrix%281%2C3%2C%0D%0Ay+=+x%5E2+-+2x%2C%22%2C%22%2C++x%3E1%29

Interchange x and y.  You can interchange them now or later. 
I prefer to do it now, but your teacher might prefer to wait
to interchange them.  It really doesn't make any difference.

matrix%281%2C3%2C%0D%0Ax+=+y%5E2+-+2y%2C%22%2C%22%2C++y%3E1%29

Solve for y by first swapping left and right sides:

matrix%281%2C3%2C%0D%0Ay%5E2+-+2y=x%2C%22%2C%22%2C++y%3E1%29

Get 0 on the right side by subtracting x from both sides:

matrix%281%2C3%2C%0D%0Ay%5E2+-+2y-x=0%2C%22%2C%22%2C++y%3E1%29

Use the quadratic formula:



matrix%281%2C3%2C%0D%0Ay=%282+%2B-+sqrt%284%2B4x%29%29%2F2%2C%22%2C%22%2C++y%3E1%29

matrix%281%2C3%2C%0D%0Ay=%282+%2B-+sqrt%284%281%2Bx%29%29%29%2F2%2C%22%2C%22%2C++y%3E1%29

matrix%281%2C3%2C%0D%0Ay=%282+%2B-+2sqrt%281%2Bx%29%29%2F2%2C%22%2C%22%2C++y%3E1%29

matrix%281%2C3%2C%0D%0Ay=%282%281+%2B-+sqrt%281%2Bx%29%29%29%2F2%2C%22%2C%22%2C++y%3E1%29



matrix%281%2C3%2C%0D%0Ay=1+%2B-+sqrt%281%2Bx%29%2C%22%2C%22%2C++y%3E1%29

Since y > 1, we must choose the + sign and discard the negative sign.
Then we don't need to keep the y > 1 because the equation guarantees
that y will always be greater than 1.

y=1+%2B+sqrt%281%2Bx%29

Next we change y to f-1(x):

f%5E%28-1%29%28x%29%22%22=%22%221%2Bsqrt%281%2Bx%29

The graph of that is the green curve below, which is the projection 
of the original (red) graph into the identity line, whose equation is y = x.



Edwin