## Meehan98 one year ago Identify the inverse of f(x) = x^2 − 4. Determine whether it is a function and state its domain and range.

1. Meehan98

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.

2. anonymous

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

3. anonymous

|dw:1441919648595:dw|

4. anonymous

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

5. Meehan98

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

6. Meehan98

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

7. Meehan98

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

8. anonymous

$$y=\sqrt{x+4}$$ 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. |dw:1441933536504:dw|