# Homework Question

• Sep 17th 2006, 09:28 AM
drewms64
Homework Question
1. Express h(x)=cos(9x^2) as a composition of two functions f and g so that h(x)= f(g(x)).

which I ended up getting
g(x)= 9x^2 and f(x)=cosx

2. Find the domain of the function f(x)= square root of (3x+1)/(5-x)

not positive what to do here, I know that the x cant be 5 since that would make the fraction undefined.
• Sep 17th 2006, 10:02 AM
TD!
Quote:

Originally Posted by drewms64
1. Express h(x)=cos(9x^2) as a composition of two functions f and g so that h(x)= f(g(x)).

which I ended up getting
g(x)= 9x^2 and f(x)=cosx

That's fine and probably also the solution that you were intended to find.

Quote:

Originally Posted by drewms64
2. Find the domain of the function f(x)= square root of (3x+1)/(5-x)

not positive what to do here, I know that the x cant be 5 since that would make the fraction undefined.

You have to watch out for two things here:
- denominators cannot become 0 since division by zero isn't defined in R.
- expressions under square roots cannot be negative, squares are nonnegative in R.

I would like to point out though that formally, the domain should be given if you want to talk about a 'function'. Better wording would have been to find the 'maximal' domain on R, sometimes called the 'natural domain'.
• Sep 17th 2006, 10:47 AM
drewms64
so for #2 then, the domain would be, x is not equal to 5 and x is greater than or equal to -1/3

one more thing, I got an answer to a problem using a difference quotient where the answer is, 3x^2+3hx+h^2+6 should I factor this further or is that good enoughf or an answer?

thanks for all of the help
• Sep 17th 2006, 11:29 AM
topsquark
Quote:

Originally Posted by drewms64
so for #2 then, the domain would be, x is not equal to 5 and x is greater than or equal to -1/3

Careful! Can x be greater than 5? (I'm assuming the 5-x is also under the square root symbol, yes?)

-Dan
• Sep 17th 2006, 01:39 PM
drewms64
yes the whole fraction is under the square root, so the domain would be, x not equal to 5, -1/3<= x< 5
• Sep 17th 2006, 02:47 PM
topsquark
Quote:

Originally Posted by drewms64
yes the whole fraction is under the square root, so the domain would be, x not equal to 5, -1/3<= x< 5

You got it! :)

-Dan