Question

100 points

The function f(x) = 2x2 + 3 represents the rate of a boat traveling with the current in miles per hour. The function g(x) = x + 2 represents the time the boat traveled in hours. Solve (f • g)(2), and interpret the answer.

(f • g)(2) = 15, the distance in miles the boat traveled
(f • g)(2) = 15, the number of boats
(f • g)(2) = 44, the distance in miles the boat traveled
(f • g)(2) = 44, the number of boats

Answer 1

Find f.g(x)

• (x+2)(2x²+3)
• 2x³+3x+4x²+6

Put 2

f.g(2)

• 2(2)³+3(2)+4(2)²+6
• 2(8)+6+6+4(4)
• 16+16+12
• 44

Option C

Answer 2

• C. (f • g)(2) = 44, the distance in miles the boat traveled

Explanation:

Given functions:

• f(x) = 2x² + 3
• g(x) = x + 2

Find the value of (f · g)(2):

• (f · g)(2) = f(2) · g(2) = (2(2²) + 3) · (2 + 2) = 11 · 4 = 44

Since this is a product of the speed and the time, this represents the distance travelled in 2 hours

Correct choice is C