• Oct 10th 2013, 08:49 PM
rhcprule3
Let F(x)=f(f(x)) and G(x)=F(x)^2 . You also know that f(8)=2, f(2)=3, f ' (2)=11, f '(8)=3

Find and .

I have no idea of where to even start on this
• Oct 10th 2013, 09:10 PM
SlipEternal
Use the chain rule. If $c(x) = a(b(x))$ for some differentiable functions $a,b$, then $c'(x) = a'(b(x))b'(x)$ by the chain rule. Do something similar to find $F'(x)$ and $G'(x)$.
• Oct 11th 2013, 04:49 AM
rhcprule3
ok so how do I set up the function to find F(x)? Is it something along the lines of F(f(x), so I would use F(f(2))=h(x)?
• Oct 11th 2013, 04:59 AM
Plato
Quote:

Originally Posted by rhcprule3
Let F(x)=f(f(x)) and G(x)=F(x)^2 . You also know that f(8)=2, f(2)=3, f ' (2)=11, f '(8)=3
Find Fhttp://webwork.morris.umn.edu/webwor...100/char30.png(8)= and Ghttp://webwork.morris.umn.edu/webwor...100/char30.png(8)=.

Quote:

Originally Posted by rhcprule3
ok so how do I set up the function to find F(x)? Is it something along the lines of F(f(x), so I would use F(f(2))=h(x)?

$F'(x)=f'(f(x))f'(x)~\&~G'(x)=2F(x)F'(x)$

Now you are give all necessary information to complete the substitutions.
• Oct 11th 2013, 05:25 AM
rhcprule3
ok but what do I do with the given functions? like for f(8)=2, do I just plug in f(8) for f(x)?
• Oct 11th 2013, 05:27 AM
rhcprule3
Like 2(f(8)8(f(3)? and i have no clue how to get G'(x). Id rather be walked through the problem so I can learn step by step how to do this problem...
• Oct 11th 2013, 05:38 AM
Plato
Quote:

Originally Posted by rhcprule3
Like 2(f(8)8(f(3)? and i have no clue how to get G'(x). Id rather be walked through the problem so I can learn step by step how to do this problem...

Well, it is evident to me that your misunderstandings are so profound that the help you need is beyond what we can give. You need to sit down with a live instructor and discuss what you can do to strengthen your understanding of the background material necessary for being successful in this course.
• Oct 11th 2013, 06:27 AM
SlipEternal
A function is like a machine. You give it input, it does something, and it gives you output. So, the notation $f(x)$ means if you give the function the input $x$, you get the output $f(x)$. So, the value of $f(x)$ when $x=8$ is just $f(8)$. If you have $F'(x) = f'(f(x))f'(x)$, then you are asked to find $F'(8)$, you just put 8 wherever you see an $x$ in $f'(f(x))f'(x)$.
Now, how do you evaluate the result $f'(f(8))f'(8)$? You use the information you are given. You are told f(8)=2, f(2)=3, f ' (2)=11, f '(8)=3. When you have an expression like $f(8)=2$, it means that if you give the machine $f(x)$ the input 8, you get back the output 2. So, $f(x)$ is a placeholder for a number. When you put a number into $x$, you get back a number. It is no longer a placeholder. $f(8)$ is a number. One of the rules of functions is that each time you give it the same input, you get the same output. So, you will never find that $f(8)=2$ the first time you plug in 8, then the next time you plug in 8, you get a different number. Once you know $f(8)=2$, you can consider $f(8)$ and $2$ to be the same number.
So, suppose you have $f(a) = b$ and you are asked to evaluate $f(f(a))$. That would be $f(f(a)) = f(b)$.