if f(x)=2x^2 -8x+10
find f^-1(x)

Question

if f(x)=2x^2 -8x+10
     find f^-1(x)

anonymous · Answer

Does that mean the inverse of f? In other words if f^-1 is the inverse of f, if y = f(x), then x = f^-1(y). 
You wont be able to solve this function for x in a way that will work for all y. This is because the function is a parabola, so can be two values of x which correspond to the same value of y. You can find an inverse that works for a limited range of y by using the quadratic formula to solve $$y = 2x^2 - 8x + 10$$ for x in terms of y, and choosing one of the solutions.

anonymous · Answer

can u pls explain it better? i dnt relly get it

anonymous · Answer

Suppose we had a function g(x) $$y = g(x) = 2x$$
We could solve this for x
$$x = \frac{ g(x) }{ 2 } = \frac{ y }{ 2 }$$
The above would be the inverse function of g,
$$x = g^{-1}(y) = \frac{ y }{ 2 }$$
But if we had a different function of x
$$y = h(x) = x^2$$
Then there is no inverse function because there are two x values for every y
$$x = \pm \sqrt{y}$$
so if we wrote$$h^{-1}(y)$$
If wouldn't be clear if that should be equal to the positive or negative value of x. But if we only use h(x) with x greater than zero, than we have an inverse
$$h^{-1} (y) = +\sqrt{y}$$
There are errors in my first post, it should say "for all x" and "limited range of x", and not y. Hopefully this is clearer

anonymous · Answer

thanks for your help but what i need is the steps involved in the working