Question

Evaluate the composition of the functions below

f(x)=3x+2
g(x)=x²-1
h(x)=x/2
f(h(12))= _______.

a) f(h(12)) = 8
b) f(h(12)) = 6
c) f(h(12)) = 7
d) f(h(12)) = 5

Answer 1

The composition f(h(12)) is calculated in two steps: first by finding h(12) as 6 and then substituting this value into f(x) to get f(6), resulting in a value of 20, which is not listed in the provided options.

Step-by-step explanation:

The question asks to evaluate the composition of the given functions, specifically to find f(h(12)). First, we need to find the value of h(12) using the function definition h(x) = x/2, and then we substitute this value into the function f(x) = 3x + 2.

1. Calculate h(12):
   
   h(12) = 12/2 = 6.
2. Substitute h(12) into f(x) to get f(h(12)):
   
   f(6) = 3(6) + 2 = 18 + 2 = 20.

The correct answer is not provided in the options a), b), c), d) above, possibly due to a typo in the question. The correct value of f(h(12)) is 20.