Question

PLEASE HELP. 10 POINTS

The function f(x) = 2x2 + 2 represents the rate of a bus traveling in miles per hour. The function g(x) = x + 2 represents the time the bus traveled in hours. Solve (f • g)(3), and interpret the answer.
A. (f • g)(3) = 100, the distance in miles the bus traveled
B. (f • g)(3) = 100, the number of buses
C. (f • g)(3) = 25, the distance in miles the bus traveled
D. (f • g)(3) = 25, the number of buses

Answer 1

Option A. (f • g)(3) = 100, the distance in miles the bus traveled

Explanation:

we have

`f(x)=2x^(2)+2`

`g(x)=x+2`

`(f*g)(x)=f(x)*g(x)`

`(f*g)(x)=(2x^(2)+2)(x+2)`

For x=3

`(f*g)(3)=(2(3)^(2)+2)(3+2)`

`(f*g)(3)=(20)(5)=100`

The units are

`(f*g)(x)=((miles)/(hour))(hour)=miles`

therefore

`(f*g)(3)=100\ miles`