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kaylaprincess

  • one year ago

help with simple subject with inverse functions ~ I don't get f^-1(x) ... What does that mean? And how do i continue to solve?

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  1. kaylaprincess
    • one year ago
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    So I looked up to understand more : take the opposite of the function. 1. Change f(x) to y 2. switch x and y 3. solve for y but what about the -1 ??

  2. kaylaprincess
    • one year ago
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    here's an example : Let f(x) = x2 - 16. Find f-1(x)

  3. kaylaprincess
    • one year ago
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    wait i think i see what im freaking out about wow lol

  4. Empty
    • one year ago
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    Yeah you did a good job of tracking down the steps of _how_ to do this, so I'll explain this so you understand what the heck this does! All the inverse function is, \(f^{-1}(x)\) is the function that you can plug into the original function to get x. This sounds weird, but here's an example: \(f(x)=x^2\) \(f^{-1}(x)=\sqrt{x}\) So now check it out, we can plug them into each other either way: \(f(f^{-1}(x))=(\sqrt{x})^2=x\) or \(f^{-1}(f(x)) =\sqrt{x^2}= x \) Don't let the negative sign disturb you, it's just a fancy bit of notation to tell you it's special. It is only to remind you it has this relationship to \(f(x)\) and doesn't actually mean anything more.

  5. Empty
    • one year ago
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    Just to be complete, I'll show how we could have solved this with that method to make it all connect up: \(f(x)=x^2\) Let's turn \(f(x)\) into \(x\) and \(x\) into \(y\) : \(x=y^2\) Solve for \(y\) \(\sqrt{x}=y\) Oh hey, this \(y\) is really our \(f^{-1}(x)\) we were talking about earlier, we're literally just undoing the function from the standpoint of x, so that's why we call it the inverse.

  6. kaylaprincess
    • one year ago
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    so for any final answer in an inverse function question, write it out with the -1? |dw:1437687398734:dw|

  7. kaylaprincess
    • one year ago
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    thank you for helping me so much by the way..!!

  8. Empty
    • one year ago
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    Yeah for my example it will be but for your example it will be slightly different! \(f(x)=x^2-16\) Go ahead and try this out by replacing f(x) with x and x with y, you'll get something a little different.

  9. kaylaprincess
    • one year ago
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    \[16x = y ^{2 } \]

  10. kaylaprincess
    • one year ago
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    ?

  11. kaylaprincess
    • one year ago
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    then take the square root ?

  12. Empty
    • one year ago
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    You're on the right track, so to get from here to here you have to add, like this: \(x=y^2-16\) Now we can add 16 to both sides, since that will keep both sides equal to each other, which is what we have to do in order to keep that = sign correctly. \(x+16=y^2 -16+16\) So now the point of that is because we both know that \(16-16=0\) on the right side there! \(x+16=y^2\) Now you can do what you said earlier and take the square root of both sides! :D

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