Posted by Jon on Wednesday, February 20, 2008 at 1:45pm.
If g(x)= 3x8, find g[g(4)].
A)68
B)4
C)20
D)52
I got C
3x8[3x8(4)]
3x8+3x+32
thats all I have

Math  Reiny, Wednesday, February 20, 2008 at 2:06pm
??
two ways to do this
1. if g(x) = 3x8
then g(g(x)) = 3(3x8)  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  Jon, Wednesday, February 20, 2008 at 2:23pm
the brackets confused me

Math  Guido, Wednesday, February 20, 2008 at 4:49pm
We have composite functions here.
You are given:
If g(x)= 3x8, 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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