State if the inverse of y=x^2-4 is a function.

Question

So, I got y= squareroot of x+4
I'm don't think it's a function because of even roots, but I'm not sure

Answer 1

Woahhh, let's back up here, how did you get that inverse?

How do you find the inverse of a function?

- you interchange the x and y variables.
so the inverse of y = x^2 + 4 is
x = y^2 + 4

- now solve this for y
y^2 = x - 4
y = ±√(x-4)

now let x = 8 , (or some other value of x you feel like)
then y = 2 or -2
so we have two points (8,2) and (8,-2)
This violates the rule of a function in that for every x I choose there can be one and only one value of y

You might also investigate the vertical line test to see if a relation is a function.

Answer 2

I solved for y and got y = ±√(x+4) for the inverse, the given equation was
y=x^2-4 not y = x^2 + 4
but your explanation helped understand why the inverse is not a function, thank you!