f(0) = we are just replacing x with 0 = sqrt (0) / (0 + 1) = 0/1 = 0
f(2) = sqrt (2) /(2 + 1) = sqrt (2) / 3
f( a + 2) = sqrt (a+2) / [ (a + 2) + 1 ] = sqrt (a + 2) / ( a + 3)
Domain
We have two things to consider .....in the numerator, x cannot be < 0
In the denominator, x cannot = -1 (we would be dividing by 0 if it were )
So we need to take the most restrictive domain.....this is [ 0 , infinity )
Avg rate of change be between 2 and 10
f(10) =sqrt (10) /(10 + 1) = sqrt (10)/ 11
f(2) =sqrt ( 2) / (2 + 1) = sqrt (2) / 3
Avg rate of change =
f(10) - f(2) sqrt (10) /11 + sqrt (2)/3
_________ = ______________________ ≈ .0949
10 - 2 8