# 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

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