Question

Identify the inverse of f(x) = x^2 − 4. Determine whether it is a function and state its domain and range.

Answer 1

I know the answer to this, but I don't understand how the inverse is not a function because I did the horizontal line test on the original function and found that it WAS a function.
The answer is (sq rt x+4); not a function
Range is all real numbers and domain is any number greater than or equal to -4.

Answer 2

f(x) = x² - 4 is a parabola, so it doesn't pass the horizontal line test. It's not one-to-one, therefore it's inverse is not a function

Answer 3

sorry, I did x²+4 instead of x² - 4.
The idea is the same, though

Answer 4

Yes, I see how x^2-4 is not a function but isn't \[\sqrt{x+4}\]

Answer 5

Sorry, isn't that a function because it passes the horizontal line test.

Answer 6

Never mind, that would be something like the inverse of the inverse. I get it now! :)

Answer 7

\(y=\sqrt{x+4}\) is only the top half of the inverse.
\(y=-\sqrt{x+4}\) is the other half.
As you can see, the original function doesn't pass the horizontal line test and the inverse (in black) doesn't pass the vertical line test.