SOLUTION: Find [f ○ (g ○ h)](2) if f(x) = 2x - 1, g(x) = 4x, and h(x) = x²+ 1 A.) 39 B.) 32 C.) 47 D.) 129

Algebra ->  Test -> SOLUTION: Find [f ○ (g ○ h)](2) if f(x) = 2x - 1, g(x) = 4x, and h(x) = x²+ 1 A.) 39 B.) 32 C.) 47 D.) 129       Log On


   

Question 1036655: Find [f ○ (g ○ h)](2) if f(x) = 2x - 1, g(x) = 4x, and h(x) = x²+ 1
A.) 39
B.) 32
C.) 47
D.) 129

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the inner most function h(x). Plug in x = 2.

h(x) = x^2+1
h(2) = 2^2+1
h(2) = 4+1
h(2) = 5

So (g o h)(2) = g(h(2)) = g(5). Let's find the value of g(5)

g(x) = 4x
g(5) = 4*5 ... plug in x = 5
g(5) = 20


That means
(g o h)(2) = g(h(2))
(g o h)(2) = g(5)
(g o h)(2) = 20

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[f o (g o h)](2) = f[ g(h(2)) ]
[f o (g o h)](2) = f[ g(5) ]
[f o (g o h)](2) = f[ 20 ]

Let's find the value of f(20)

f(x) = 2x - 1
f(20) = 2*20 - 1
f(20) = 40 - 1
f(20) = 39


The final answer is A) 39.