Math Help - Functions confusion

1. 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

2. Re: Functions confusion

Also...

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.)

3. Re: Functions confusion

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

For example, take $f(x) = 3x + 2$ and $g(x) = \frac{1}{x}$

Then
$f \circ g(x) = f(g(x)) = f \left ( \frac{1}{x} \right ) = 3 \left ( \frac{1}{x} \right ) + 2$

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

-Dan

Thanks

5. Re: Functions confusion

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.