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.