Math

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If g(x)= 3x-8, find g[g(-4)].

A)-68
B)4
C)-20
D)52
I got C

3x-8[3x-8(-4)]
3x-8+3x+32
thats all I have

  • Math -

    ??

    two ways to do this

    1. if g(x) = 3x-8
    then g(g(x)) = 3(3x-8) - 8 = 9x - 30
    then g(g(-4)) = 9(-4)-30 = -68

    2. first find g(-4) = 3(-4)-8 = -20

    then g(g(-4)) = g(-20) = 3(-20) - 8 = -68

  • Math -

    the brackets confused me

  • Math -

    We have composite functions here.

    You are given:

    If g(x)= 3x-8, find g[g(-4)].

    By the way, g[g(-4)] can also be written g(g(-4)) and it's read:

    "g of g of negative four."

    We are looking for g of g of x first.

    To do so, replace x in (3x - 8) with the value (3x - 8) as step one. In other words, find g(g(x)) first.

    g(3x - 8) = 3(3x - 8) - 8

    g(3x - 8) = 9x - 24 - 8

    g(3x - 8) = 9x -32

    This means that "f of g of x" =
    9x - 32.

    We now replace x with -4 in 9x - 32 and simplify.

    g(g(-4)) = 9(-4) - 32

    g(g(-4)) = -36 - 32

    g(g(-4)) = -68

    Answer is: Choice (A)

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