can some one explain this to me let f(x)=x squared -81. FInd f1(x)

Question

accessdenied · Answer

Do you mean to find $f^{-1} (x) $  ?

anonymous · Answer

no that is what the question says thats why im confused

anonymous · Answer

$$f(x)=x ^{2}-81 find f ^{1}(x)$$

accessdenied · Answer

What topic are you working on in Math?  Maybe it is $f'(x) $, as in the derivative of f(x) with respect to x?

anonymous · Answer

functions

accessdenied · Answer

Hm... I do not know what that notation is supposed to mean, then.  I want to say it is a typo for inverse function of f.  Are there answer choices with this problem as well?

anonymous · Answer

yes the answer choices are

anonymous · Answer

$$\pm \sqrt{x+81}$$

anonymous · Answer

$$9\sqrt{x}$$

anonymous · Answer

$$1/x ^{2}-81$$

anonymous · Answer

$$x ^{2}/81$$

accessdenied · Answer

Alright.  I definitely believe this is meant to be $f^{-1} (x) $ of $f(x) = x^2 - 81$ now, as I can see the answer among the choices.
You know how to find inverse functions?

anonymous · Answer

i don't now how to do it when there is a number behind the $$x ^{2}$$

accessdenied · Answer

Have you seen this method?  We switch $f(x)$ for x, and x for $f^{-1}(x) $ in the equation.
$x = \left( \color{blue}{f^{-1}(x)} \right)^2 - 81 $
Where we just have to solve for the function like we would any variable:
$x = \color{blue}{y}^2 - 81 $

anonymous · Answer

i have never seen the first method but have seen the second method

accessdenied · Answer

They're basically the same, but I'll continue writing with y.
  $ x = y^2 - 81 $
We first solve for the y^2.  We can do that by adding 81 to both sides, cancelling the -81 next to y^2.  Then take the positive and negative square root of both sides.  That would get y by itself with no powers.

anonymous · Answer

how would you take to square root of x+81

accessdenied · Answer

We wouldn't need to simplify it, we just leave it like this:
  $ \pm \sqrt{x + 81} = y $
We can take the square root, even if the left side doesn't necessarily simplify nicely like square root of 9 = 3.  Like if we had 6 = y^2,  we could take + or - sqrt(6) = y without having to simplify 6.  It is the same with x + 81.  :)

anonymous · Answer

oh ok so wouldn't that be the answer

accessdenied · Answer

Yes, that should be the answer.  :)

anonymous · Answer

ok thank you so much

accessdenied · Answer

Glad to help!