I need help with this question

7

Step-by-step explanation:

1. Approach

The average rate of change can simply be defined as the slope of a line that passes through any two points on a coordinate plane. In this situation, one is given a function, and one is asked to find the rate of change over an interval.

Given function:

Intervale,

This can be done by evaluating the endpoints of the interval by substituting them into the function. Then writing the resulting the form of a point on the coordinate plane (). Finally, one can find the slope of the line that passes through the points by using the following slope formula,

Where () and () are coordinate points.

2. Find the points

With the function (f(x)), substitute the end points of the itnerval ( [0, 4] ) into the function to generate coordinate points,

[ 0, 4 ]

Point: (0, 0)

Point: (4, 28)

3. Find the average rate of change,

Now substitute the points the formula to find the slope, then simplify to evaluate

(0, 0), (4, 28)

Substitute,

The average rate of change is 7.

step-by-step explanation:

f(gx)=f(1/x+2)

=(1/x+2)+2

=(1+2x)/2+2

=(1+2x+4)/2

= (2x+5)/2