f(x)= x/(x^2-4)
The domain for this function is restricted to -2<x<2
Can anyone help with this? Thanks!
Well I got that, but I'm unsure as to which one it is. I have a feeling that its the second one (the one with the negative sign) because when I made data tables, the x and y values were switched, but there has to be an easier method. Can anyone help?
And thanks skeeter!
Hello, MegaVortex7!
I had to baby-talk my way through this one . . .
The domain for this function is restricted to
Find the inverse function,
To visualize the effect of the domain, I graphed the function.Code:: | : :* | : : | : : * | : : * | : : * | : : * | : - - + - - - - - * - - - - - + - - -2: | * :2 : | * : : | * : : | * : : | : : | *: : | :
Then the inverse function looks like this:To find the inverse . . .Code:| - - - - - - - - + - - - - - - - - * |2 * | * | * | *| | - - - - - - - - - * - - - - - - - - - | |* | * | * | * | * - - - - - - - - + - - - - - - - - - - |-2
Replace with
Switch 's and 's: .
Solve for
. .
Quadratic Formula: .
If the inverse is to resemble its graph above,
. . (as x → +∞, y → -2)
. . we must have: .
Nice and simple but then the OP has to be sophisticated enough to realise that you make the choice that gives an indeterminant form. This choice should be obvious since the other choice gives something undefined. Nevertheless, I'd predict hand wringing and angst with this choice .......