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Math Help - Homework Question

  1. #1
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    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.
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  2. #2
    TD!
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    Quote Originally Posted by drewms64 View Post
    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 View Post
    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'.
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  3. #3
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    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
    Last edited by drewms64; September 17th 2006 at 11:30 AM.
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  4. #4
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    Quote Originally Posted by drewms64 View Post
    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
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  5. #5
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    yes the whole fraction is under the square root, so the domain would be, x not equal to 5, -1/3<= x< 5
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  6. #6
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by drewms64 View Post
    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
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