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

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

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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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.
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
|dw:1441919648595:dw|

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sorry, I did x²+4 instead of x² - 4. The idea is the same, though
Yes, I see how x^2-4 is not a function but isn't \[\sqrt{x+4}\]
Sorry, isn't that a function because it passes the horizontal line test.
Never mind, that would be something like the inverse of the inverse. I get it now! :)
\(y=\sqrt{x+4}\) 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|

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