# Determine arithmetic mean of the numbers f(x1), f(x2) for f(x) = x/2-6 ; x1 = -8, x2 = 10

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f(x) = x/2-6 x1 = -8. x2 = 10.

To find the arithmetic mean of f(x1) and f(x2).

f(x1) =f(8) = -8/2-6

f(-8) = -4-6

f(-8) = -10

f(x2) = f(10)

f(10) = 10/2-6

f(10) = 5-6

f(10) = -1.

Therefore the arithmetic mean of f(x1) and f(x2) = {f(x1)+f(x2)}/2 = {f(-8) + f(10)}/2

{f(-8)+f(10)}/2 = {-10-1}/2 = -5.5.

Therefore the arithmetic mean of f(-8) and f(10) is -5.5.

We'll determine the arithmatic mean of the numbers f(x1) and f(x2):

A.M. = [f(x1) + f(x2)]/2

To compute the value of A.M., we'll have to compute the values of f(x1) and f(x2).

For this reason, we'll substitute x1 and x2 in the expression of f(x).

For x1 = -8, we'll get:

f(-8) = -8/2 - 6

f(-8) = -4 - 6

f(-8) = -10

For x2 = 10, we'll get:

f(10) = 10/2 - 6

f(10) = 5 - 6

f(10) = -1

Now, we'l substitute f(x1) and f(x2) by the values of f(-8) and f(10) in the expression of A.M.

A.M. = [f(-8) + f(10)]/2

A.M. = (-10-1)/2

**A.M. = -11/2**