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Math Help - function composition

  1. #1
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    function composition

    "If f(x) = 4x, g(x) = 2x 1 and h(x) = x2 + 1, find each value."
    a. h[g(4)]

    b. f[f(-3)]

    c. g[h(-1/2)]

    d. [f ○ (h ○ g)](3)

    I don't really know where to start with this question so any help on it would really be appreciated.



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  2. #2
    tah
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    a) first calculate g(4) (replacing x by 4 in the expression of g(x)), and then calculate the h of that value.
    idem for b) c)

    d) f\circ g(x) = f[g(x)], so what is [f\circ (h\circ g)](x) ? and use the same reasoning as in a)
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  3. #3
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    not factoring ... this is function composition.

    a. h[g(4)]

    first calculate g(4) ...

    g(x) = 2x - 1

    g(4) = 2(4) - 1 = 7

    h[g(4)] = h(7) = (7)^2 + 1 = 50

    you do b and c.

    d. [f ○ (h ○ g)](3) = f[h[g(3)]]

    start by evaluating g(3) , then h[g(3)], then f[h[g(3)]] ... work inside out.
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