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What is (f-g)(x) for the function f(x)=3x+2 and g(x)=x^x-6x+1 when x=3?

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Explanation:

To find (f-g)(x) for the given functions, we need to substitute the function expressions into the expression for (f-g)(x) and evaluate it at x=3.

(f-g)(x) = f(x) - g(x)

Given:

f(x) = 3x + 2

g(x) = x^x - 6x + 1

x = 3

Substituting the expressions for f(x) and g(x), we get:

(f-g)(x) = (3x + 2) - (x^x - 6x + 1)

Substituting x=3, we get:

(f-g)(3) = (3*3 + 2) - (3^3 - 6*3 + 1)

Simplifying the calculation, we get:

(f-g)(3) = 9 + 2 - 26

(f-g)(3) = -15

Therefore, (f-g)(x) for the given functions when x=3 is -15.

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