For f(x) =4x+1 and g(x) = x^2 - 5 find (f•g)(x)

a.4x^3+x^2 -20x-5
b.4x^2-19
c.4x^3 + x^2-4x-6
d.4x^3+x^2-5x-5

The value of function (fog)(x) is 4 x² - 19

Step-by-step explanation:

Given function as :

f(x) = 4 x + 1

g(x) = x² - 5

So , function (fg(x)) can be written as

     (fog)(x) = 4 ( x² - 5 ) + 1

Or, (fog)(x) = 4 x² - 20 + 1

Or, (fog)(x) = 4 x² - 19

Hence The value of function (fog)(x) is 4 x² - 19    Answer

a) Jo started coming back to the original starting point.

b) Average Speed of Jo for 30 minutes was 11.11 m/s.

Step-by-step explanation:

From the given graph, we can see that

1. From time 0 to 10 minutes, the distance is increasing i.e. Jo is moving away from the starting point.

2. From time 10 to 20 minutes, the distance is decreasing i.e. Jo has started moving back to the starting point where Jo was at time 0 minutes.

3. From 20 minutes to 30 minutes, Jo was at rest.

4. At 30 minutes of time, Jo started moving further at a constant speed (as represented by the straight line).

Part a) When we look at the graph, at time 10 minutes, the line started coming back towards the zero of y axis i.e. distance.

So, Jo started coming back towards his original starting point where Jo was at time 0 minutes.

b)

Time 0 to 10, distance traveled = 1 km

Speed at this time =

Time 10 to 20, distance traveled = 1 km

Speed at this time =

Time 20 to 30, distance traveled = 0 km

Speed from time 0 to 30 minutes: