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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?
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?

This Question is Closed

kaylaprincess
 one year ago
Best ResponseYou've already chosen the best response.1So 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 ??

kaylaprincess
 one year ago
Best ResponseYou've already chosen the best response.1here's an example : Let f(x) = x2  16. Find f1(x)

kaylaprincess
 one year ago
Best ResponseYou've already chosen the best response.1wait i think i see what im freaking out about wow lol

Empty
 one year ago
Best ResponseYou've already chosen the best response.2Yeah 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.

Empty
 one year ago
Best ResponseYou've already chosen the best response.2Just 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.

kaylaprincess
 one year ago
Best ResponseYou've already chosen the best response.1so for any final answer in an inverse function question, write it out with the 1? dw:1437687398734:dw

kaylaprincess
 one year ago
Best ResponseYou've already chosen the best response.1thank you for helping me so much by the way..!!

Empty
 one year ago
Best ResponseYou've already chosen the best response.2Yeah for my example it will be but for your example it will be slightly different! \(f(x)=x^216\) Go ahead and try this out by replacing f(x) with x and x with y, you'll get something a little different.

kaylaprincess
 one year ago
Best ResponseYou've already chosen the best response.1\[16x = y ^{2 } \]

kaylaprincess
 one year ago
Best ResponseYou've already chosen the best response.1then take the square root ?

Empty
 one year ago
Best ResponseYou've already chosen the best response.2You're on the right track, so to get from here to here you have to add, like this: \(x=y^216\) 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 \(1616=0\) 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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