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Math Help - Several Algebra/Trig ? Need Help Please

  1. #1
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    Several Algebra/Trig ? Need Help Please

    Anyone,

    If you could help me with several questions that I have. They are as follows:

    1) What is the range of (fog)(x) if f(x) = x(squared) + 3 and g(x) = x+4

    2) What is g(x) =f-1(x) (the one is supposed to be for inverse not a negative number) if f(x) = 1/2x

    3) Consider g(x) =(x+2)(cubed) + 3; what is the new equation for g(x) if it is shifted up 6 units and shifted right nine units

    4) What is the range of (fog)(x) if f(x) = x(squared) + 3 and g(x) = x+4

    5) What is f(x) if f(x) = z(x) +2 and z(x) = 2x-3

    Any Help on these questions would be most appreciated.
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  2. #2
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    Joined
    May 2008
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    1. f(g(x)) = y = (x+4)^2 + 3 = x^2 + 8x + 19

    dy/dx = 2x + 8

    2x + 8 = 0, x = -4

    f(g(-4)) = 16 - 32 + 19 = 19 - 16 = 3

    So the range is f(g(x)) >= 3
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