Meehan98
  • Meehan98
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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SOLVED
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schrodinger
  • schrodinger
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Meehan98
  • 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.
anonymous
  • 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
anonymous
  • anonymous
|dw:1441919648595:dw|

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anonymous
  • anonymous
sorry, I did x²+4 instead of x² - 4. The idea is the same, though
Meehan98
  • Meehan98
Yes, I see how x^2-4 is not a function but isn't \[\sqrt{x+4}\]
Meehan98
  • Meehan98
Sorry, isn't that a function because it passes the horizontal line test.
Meehan98
  • Meehan98
Never mind, that would be something like the inverse of the inverse. I get it now! :)
anonymous
  • 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|

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