Answer:
(f.g) (2) = 27 represents the distance in miles traveled by bicycle in hour.
Step-by-step explanation:
Here, f (x) : The rate of bicycle travelling in miles per hour
and [tex]f(x) = 2x^{2} + 1[/tex]
Also, g(x): The time bicycle traveled in hours
and g(x) = x+1
Now, f . g (x) = f (g(x))
Also, distance = speed x time = f * g = f(x) g(x)
or,
[tex]f(x).g(x) = (2x^{2} +1)(x+1) = 2x^{3} +2x^{2} + x + 1\\\impliesf(x).g(x) = 2x^{3} +2x^{2} + x + 1[/tex]
⇒[tex](f.g)(2) = 2(2)^{3} + 4(2) + 2 + 1 = 16+ 8 + 3 = 27[/tex]
So, here, (f.g)(2) = 27
Hence, (f.g) (2) = 27 represents the distance in miles traveled by bicycle in hour.
Answer:
Option D.
Step-by-step explanation:
The function f(x) represents the rate of a bicycle traveling in miles per hour.
[tex]f(x)=2x^2+1[/tex]
The function g(x) represents the time the bicyclist traveled in hours.
[tex]g(x)=x+1[/tex]
We need to find the value of (f • g)(2).
Substitute x=2 in both function.
[tex]f(2)=2(2)^2+1=2(4)+1=8+1=9[/tex]
[tex]g(2)=2+1=3[/tex]
Now,
[tex](f\cdot g)(2)=f(2)\cdot g(2)[/tex]
[tex](f\cdot g)(2)=9\cdot 3[/tex]
[tex](f\cdot g)(2)=27[/tex]
Since (f • g) is product of rate of a bicycle traveling in miles per hour and number of hours, therefore (f • g) represents the distance in miles the bicycle traveled.
Hence, the correct option is D.
