Use the given functions to find each of the following and their respective domains. Do not try to simplify the resulting functions and be sure to write each domain using interval notation.
f(x)=-5x^2-5x-8 and g(x)=-x+1
(f+g)(x)=
(f-g)(x)=
(fg)(x)=
(f/g)(x)=
To find each of the following functions, we need to apply the given operations to the functions f(x) and g(x). Remember, (f+g)(x) means f(x) + g(x), (f-g)(x) means f(x) - g(x), (fg)(x) means f(x) * g(x), and (f/g)(x) means f(x) / g(x).
1. (f+g)(x)
(f+g)(x) = f(x) + g(x) = (-5x^2 - 5x - 8) + (-x + 1) = -5x^2 - 6x - 7
Domain: All real numbers
2. (f-g)(x)
(f-g)(x) = f(x) - g(x) = (-5x^2 - 5x - 8) - (-x + 1) = -5x^2 - 4x - 9
Domain: All real numbers
3. (fg)(x)
(fg)(x) = f(x) * g(x) = (-5x^2 - 5x - 8) * (-x + 1) = 5x^3 + 10x^2 + 3x + 8
Domain: All real numbers
4. (f/g)(x)
(f/g)(x) = f(x) / g(x) = (-5x^2 - 5x - 8) / (-x + 1)
To find the domain, we need to consider the values of x that make the denominator, (-x + 1), equal to zero. So, x cannot be equal to 1.
Domain: x ≠ 1