Inverse will values not a function

G

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f and g are an inverse pair

f(2)=4 f(5)=3
f'(2)=8 f'(5)= -4
g(2)=9 g(5)=-4

Determine or Explain where there is not enough information to determine

A) g'(2) B) g'(3)

Glancing at this, I immediately thought these can not be determined because there we don't know f'(x). However, I can't imagine it is that easy. Can someone set me straight on this? Thanks.[/tex][/list]
 
I assume you mean f'(x) is the inverse of f(x). That's odd notation, but we can go with it if that is your intent.

If f and g are inverse pairs, then g IS f'. That doesn't help your argument much, does it?

g'(2) = f(2) = 4
g'(3) = f(3) = Sorry, no such information is given.
 
how does g'(x)=f(x)

not inverse but derivative. so how does g'(2)=f(2)
 
That's what I was asking. Do you mean INVERSE when you use the "prime" notation? If so, then I showed you how to do it. If you mean DERIVATIVE when you use the "prime" notation, then I didn't show you anything. Just checking.

You should have this valuable result. If \(\displaystyle y = f^{-1}(x)\), then (dy/dx)(df/dy) = 1.

To find g'(2) find 1/f'(9)
To find g'(3) find 1/f'(5)
 
When I find those I get the answers. But, I would like to understand this, not just do it.

First, I am using the prime notation for derivative not inverse. If that helps...

So why would I need to find 1/f'(9) for solve for g(2). If I understand that, I can do others like it.

Thanks
 
You must ponder the "valuabe result".

f and g are inverses
If f(2) = 9 then g(9) = 2. The slopes are related, not just the locations.
 
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