Answer:
f(x) = 4 - x and g(x) = x^2 - 3x
f+g = f(x) + g(x) = (4 - x) + (x^2 - 3x) = x^2 - 4x + 4
The domain of f+g is all real numbers(-∞, ∞).
f-g = f(x) - g(x) = (4 - x) - (x^2 - 3x) = -x^2 + 7x - 4
The domain of f-g is all real numbers(-∞, ∞).
fg = f(x) * g(x) = (4 - x) * (x^2 - 3x) = -x^3 + 3x^2 + 4x
The domain of fg is all real numbers(-∞, ∞).
f/g = f(x) / g(x) = (4 - x) / (x^2 - 3x), x≠0 and x≠3
The domain of f/g is all real numbers except 0 and 3. So, it can be written as (-∞, 0) ∪ (0, 3) ∪ (3, ∞).
Note: We excluded 0 and 3 from the domain of f/g because g(0) = 0 and g(3) = 0, which makes the denominator zero.
Explanation: