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Math Help - Forming the Compositions f(g(h(x)))

  1. #1
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    Forming the Compositions f(g(h(x)))

    Hello MHF

    So I have been working with functions. They have been pretty simple so far.

    Like...
    EXAMPLE: Form the composition f(g(x)) and give the domain:
    f(x) = 2^2 + x
    g(x) = sqrt(x)

    So f(g(x)) = [sqrt(x)]^2 + sqrt(x) = x + sqrt(x)

    Therefore domain is [0,+inf)

    BUT what if we have3 functions and we are trying to create a composition? I just want to make sure I am doing this right...

    EXAMPLE: Form the composition f(g(h(x))) and give the domain:

    f(x) = x -1
    g(x) = 4x
    h(x) = x^2

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

    Therefore domain is (-inf,+inf).

    Can someone confirm that I did the triple composition correctly?
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  2. #2
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    Quote Originally Posted by UC151CPR View Post
    Hello MHF

    So I have been working with functions. They have been pretty simple so far.

    Like...
    EXAMPLE: Form the composition f(g(x)) and give the domain:
    f(x) = 2^2 + x
    g(x) = sqrt(x)

    So f(g(x)) = [sqrt(x)]^2 + sqrt(x) = x + sqrt(x)

    Therefore domain is [0,+inf)

    BUT what if we have3 functions and we are trying to create a composition? I just want to make sure I am doing this right...

    EXAMPLE: Form the composition f(g(h(x))) and give the domain:

    f(x) = x -1
    g(x) = 4x
    h(x) = x^2

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

    g(x^2) = 4x^2, not 4x^3

    Therefore domain is (-inf,+inf).

    Can someone confirm that I did the triple composition correctly?
    ...
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  3. #3
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    Oops

    Oh yah, my mistake. I accidently wasn't thinking and multiplied x by 4x^2 instead of just substituting it, so I should have gotton

    4x^2 - 1 as the composition

    thanks
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