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Math Help - Composition,Domain,Notation?

  1. #1
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    Composition,Domain,Notation?

    (a)
    Let f(x) = |x - 2|, g(x) = √x (square root of x) and h(x) = x^-1 (x to the power of -1).
    Find the following COMPOSITIONS and state their DOMAIN in INTERVAL NOTATION:
    (i) f ○ g
    (ii) h ○ g
    (iii) (h ○ g) ○ f


    (b)
    Let f(x) = 1 sin(x + π).
    Express f(x) as a COMPOSITIONS of three functions (in the right order!) and state the DOMAIN of f in SET NOTATION.


    The question asks part (a) compostion & domain in interval notation.
    Part (b) asks composition & domain in set notation.

    { } ∩ U ] [ ( ) | ≤ ≥ ∞ Є ○ π
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  2. #2
    GAMMA Mathematics
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    Quote Originally Posted by federer View Post
    (a)
    Let f(x) = |x - 2|, g(x) = √x (square root of x) and h(x) = x^-1 (x to the power of -1).
    Find the following COMPOSITIONS and state their DOMAIN in INTERVAL NOTATION:
    (i) f ○ g
    (ii) h ○ g
    (iii) (h ○ g) ○ f


    (b)
    Let f(x) = 1 sin(x + π).
    Express f(x) as a COMPOSITIONS of three functions (in the right order!) and state the DOMAIN of f in SET NOTATION.


    The question asks part (a) compostion & domain in interval notation.
    Part (b) asks composition & domain in set notation.

    { } ∩ U ] [ ( ) | ≤ ≥ ∞ Є ○ π
    f(x) = |x-2|
    g(x) = \sqrt{x}

    f[g(x)] = |\sqrt{x}-2|

    It's domain is all non-negative numbers because you cannot take the square root of a negative number.
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