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
the brackets confused me
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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