# Thread: inverse function, solving for x with two variables

1. ## inverse function, solving for x with two variables

Hello,

I need to find the inverse function (finding f^-1) of f(x)= sqrt[3-x].

So I figured y = sqrt[3-x]

then solve for x to get x = 3- y^2 (?) when I graph it does not look like the inverse.

2. What you did is half correct. You just have to switch the y and the x to get the inverse function.

3. Originally Posted by Chop Suey
What you did is half correct. You just have to switch the y and the x to get the inverse function.
Originally Posted by 2clients
Hello,

I need to find the inverse function (finding f^-1) of f(x)= sqrt[3-x].

So I figured y = sqrt[3-x]

then solve for x to get x = 3- y^2 (?) when I graph it does not look like the inverse.

As Chops mentioned, just swap the x and y values of the function:

$y=\sqrt{3-x}\rightarrow x=\sqrt{3-y}$

Then solve for y to find $f^{-1}(x)$.

--Chris

4. Don't forget the restriction on the domain of the inverse: $y = \sqrt{3-x} \geq 0$ meaning that when you interchange x's and y's, then the 'new' x is greater than or equal to 0.