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
??
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)
To find g[g(-4)], we first need to substitute -4 into the function g(x) and find the value.
g(x) = 3x - 8
Substituting -4 into g(x), we get:
g(-4) = 3(-4) - 8
= -12 - 8
= -20
Now, we substitute the result (-20) back into the function g(x):
g[g(-4)] = g(-20)
= 3(-20) - 8
= -60 - 8
= -68
Therefore, the correct answer is A) -68.