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Math Help - domains of functions

  1. #1
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    domains of functions

    f(x)=x^3-x^2+4 and g(x)=x^2-1
    find:
    -the domain of (f/g)(x)
    -f(g(x))


    thanks!!
    also what does the x have to do with finding the answers when they tell you to find (f/g)(x) ??
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  2. #2
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    Quote Originally Posted by ss103 View Post
    f(x)=x^3-x^2+4 and g(x)=x^2-1
    find:
    -the domain of (f/g)(x)
    -f(g(x))


    thanks!!
    also what does the x have to do with finding the answers when they tell you to find (f/g)(x) ??
    Hi

    \frac{f}{g}(x) = \frac{f(x)}{g(x)}

    \frac{f}{g} is defined for all values of x for which g(x) \neq 0

    g(x) = x^2 - 1 = (x+1)(x-1) is equal to 0 for x=-1 or x=1

    f(g(x)) = f(x^2 - 1) = (x^2 - 1)^3-(x^2 - 1)^2+4

    f(g(x)) = x^6 - 3x^4 + 3x^2 - 1 - x^4 +2x^2 - 1 + 4

    f(g(x)) = x^6 - 4x^4 + 5x^2 + 2
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  3. #3
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    thank you! but what would the domain be in interval notation?
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  4. #4
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    g(x) is equal to 0 for x=-1 or x=1

    Therefore the domain of f/g is ]-oo,-1[ U ]-1,1[ U ]1,+oo[
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  5. #5
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    Quote Originally Posted by ss103 View Post
    f(x)=x^3-x^2+4 and g(x)=x^2-1
    find:
    -the domain of (f/g)(x)
    -f(g(x))


    thanks!!
    also what does the x have to do with finding the answers when they tell you to find (f/g)(x) ??

    1) Think of as: \frac{x^3-x^2+4}{x^2-1}. So one can that x\neq 1, -1.

    2) f(g(x)) no problem with any x value. So the domain is \mathbb{R}.
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