Thread: Functions confusion

Hi I just have no clue where to start for this questions :S

Find the functions and their domains. (Enter the domains in interval notation.)

f(x) = x + 1/x, g(x) = x+14/x+2


(a) f g

(f g)(x)	=
domain

(b) g f

(g f)(x)	=
domain

(c) f f

(f f)(x)	=
domain

(d) g g

(g g)(x)	=
domain

Also...
Thanks a ton in advance

Find each of the following functions.
f(x) = 2 − 4x, g(x) = cos x
(a) f of g


State the domain of the function. (Enter your answer using interval notation.)


(b) g of f


State the domain of the function. (Enter your answer using interval notation.)


(c) f of f


State the domain of the function. (Enter your answer using interval notation.)


(d) g of g


State the domain of the function. (Enter your answer using interval notation.)

These a composition problems. What you need to do is to specify the two functions and "nest" one inside the other.

For example, take and

Then


Give it a try. If you still have problems show us what you have tried and we'll work from there.

-Dan

Thanks

You have to write these types of functions as f of g= f(g(x))
Thus for any type of value you have to put the value of x step by step. for the first question
(a) f of g=f(g(x))
Here, f(x)=2-4x
g(x)=cosx
Therefore, f(g(x))=f((cosx))
=>2-4cosx
These types of questions are easy to solve. you can try the other three easily.