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Math Help - Composite functions question

  1. #1
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    Composite functions question

    State the domain of f g(x) and g f(x) if f(x) = √x and g(x) = 2x - 4

    I'm just starting to work with composite functions, I have the solution to this question, but I cannot grasp how it works, can someone please give me some pointers? Here's the answer:


    f g(x) = f(g(x))
    =f(2x-4)
    =
    √(2x-4)***
    f g(x) is defined as long as 2x - 4 0 ; 2x 4 ; x 4/2 ; x 2
    the domain of f g(x) is {x | x 2, x R}

    g f(x) = g(f(x))
    =g(√x)
    =2(√x) - 4***
    g f(x) is defined as long as x 0
    the domain of g f(x) is {x | x ≥ 0, x R}

    ***These marked parts are where I am becoming confused, I can't figure out what is being done to 2x-4 to make
    √(2x-4), or what is being done to √x to make 2(√x) - 4.
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  2. #2
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    Re: Composite functions question

    Quote Originally Posted by Lethargic View Post
    State the domain of f g(x) and g f(x) if f(x) = √x and g(x) = 2x - 4

    Assuming that the functions are mapping on the same set then:
    \text{Dom}(f\circ g)=\text{Dom}(f)\cap\text{Dom}( g)
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