I don't understand these types of problems-

Find the average rate of change of f between 1 and x

f(x)-f(1)/x-1

and X cannot be equal to 1

1) f(x)= the square root of x+3

2) f(x)=1/(x^2)

3) f(x)=x^3 + x

To find the average rate of change of a function between two points, you need to calculate the difference in the function values at those points and divide it by the difference in the input values. In this case, you need to find the average rate of change of each function between 1 and x, where x cannot be equal to 1.

1) For f(x) = √(x + 3):
To find the average rate of change, substitute the given values into the formula:
[(f(x) - f(1)) / (x - 1)]
= [√(x + 3) - √(4)] / (x - 1)
Simplify the numerator by simplifying the square roots if possible.
= (√(x + 3) - 2) / (x - 1)

2) For f(x) = 1 / (x^2):
Substitute the given values into the formula:
[(f(x) - f(1)) / (x - 1)]
= [(1 / (x^2)) - (1 / 1^2)] / (x - 1)
= (1 / x^2 - 1) / (x - 1)
Simplify if necessary.

3) For f(x) = x^3 + x:
Substitute the given values into the formula:
[(f(x) - f(1)) / (x - 1)]
= [(x^3 + x) - (1^3 + 1)] / (x - 1)
= (x^3 + x - 2) / (x - 1)
Simplify further if required.

Remember, when calculating the average rate of change, it is crucial to exclude x = 1 from the calculation since that would result in division by zero.