Question

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?

Answer 1

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 ??

Answer 2

here's an example : Let f(x) = x2 - 16. Find f-1(x)

Answer 3

wait i think i see what im freaking out about wow lol

Answer 4

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.

Answer 5

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.

Answer 6

so for any final answer in an inverse function question, write it out with the -1?