To find f - g, we subtract the function g(x) from the function f(x).
Given:
f(x) = 7x + 2
g(x) = x^2 + x - 6
To find f - g, we subtract g(x) from f(x) by subtracting the corresponding terms:
(f - g)(x) = f(x) - g(x)
(f - g)(x) = (7x + 2) - (x^2 + x - 6)
Next, we simplify the expression by combining like terms:
(f - g)(x) = 7x + 2 - x^2 - x + 6
Rearranging the terms, we have:
(f - g)(x) = -x^2 + 6x - x + 2 + 6
Combining like terms again, we get:
(f - g)(x) = -x^2 + 5x + 8
Therefore, the function f - g is given by:
f - g = -x^2 + 5x + 8