1. ## fucntion inverse

consider the function of f(x)=(x-1)^2+2

1.determine the inverse of f(x)

2. Originally Posted by william
consider the function of f(x)=(x-1)^2+2

1.determine the inverse of f(x)
Solve for y:

$\displaystyle x = (y - 1)^2 + 2$.

Then $\displaystyle y = f^{-1}(x)$.

3. I think it should be pointed out that this particular function does NOT have an inverse.

4. Originally Posted by HallsofIvy
I think it should be pointed out that this particular function does NOT have an inverse.
Actually it does have an inverse. It's just that the inverse is not a function.

5. Originally Posted by mr fantastic
Actually it does have an inverse. It's just that the inverse is not a function.
Okay, but that's a different terminology from what I would consider standard. The "inverse of a function", f, is the function $\displaystyle f^{-1}$ such that $\displaystyle f(f^{-1}(x))= x$ for all x in the domain of $\displaystyle f^{-1}$ and $\displaystyle f^{-1}(f(x))= x$ for all x in the domain of f.