Question

PLS HELP 100 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.

(f ⋅ g)(3) = 100, the distance in miles the bus traveled
(f ⋅ g)(3) = 100, the number of buses
(f ⋅ g)(3) = 25, the distance in miles the bus traveled
(f ⋅ g)(3) = 25, the number of buses

Answer 1

(f ⋅ g)(3) = 100, the distance in miles the bus traveled

Explanation:

The product of (miles/hour) and (hours) is (miles), so only answers with units of distance are applicable. The numbers are ...

f(3) = 2·3² +2 = 20 . . . . miles per hour

g(3) = 3+2 = 5 . . . . hours

so (f·g)(3) = f(3)·g(3) = 20·5 = 100 . . . . miles

Answer 2

(f ⋅ g)(3) = 100, the distance in miles the bus traveled.

Explanation:

Given functions:

`\begin{cases}f(x)=2x^2+2\\g(x)=x+2\end{cases}`

To calculate the composite function (f ⋅ g)(3), multiply function f(3) by function g(3).

`\begin{aligned}(f \cdot g)(3)&=f(3) \cdot g(3)\\&=(2(3)^2+2)(3+2)\\&=(2(9)+2)(3+2)\\&=(18+2)(3+2)\\&=(20)(5)\\&=100\end{aligned}`

If function f(x) represents the rate of a bus travelling in miles per hour,

and function g(x) represents the time the bus travelled in hours:

`\implies f(x) \cdot g(x)=\rm miles/hour \cdot hour=(miles)/(hour) \cdot hours=miles=distance`

Therefore, (f ⋅ g)(3) = 100 represents the distance in miles the bus traveled.