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

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sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to average the numbers `f(-8)` and `f(10)` , hence, you need to add the numbers and divide the sum by 2, such that:

`bar (f(x)) = (f(-8) + f(10))/2`

`bar (f(x)) = ((-8)/2 - 6 + 10/2 - 6)/2`

`bar (f(x)) = (-4 - 12 + 5)/2`

`bar (f(x)) = -11/2 = -5.5`

Hence, evaluating the mean of the numbers `f(-8)` and `f(10)` , yields bar `(f(x)) = -5.5.`

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

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We'll use the identity to evaluate the arithmetic mean of the numbers f(x1) and f(x2):

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

First, we need to evaluate 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'll replace 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

The requested value of the arithmetic mean is: A.M. = -11/2

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