To find (f+g)(x), we need to add the functions f(x) and g(x):
(f+g)(x) = f(x) + g(x)
= (-3x^2 - 9x) + (9x + 4)
= -3x^2 - 9x + 9x + 4
= -3x^2 + 4
The domain of (f+g)(x) is the same as the domain of f(x) and g(x). Since there are no restrictions in the given functions, the domain is all real numbers. Therefore,
(f+g)(x) = -3x^2 + 4
d = (-∞, ∞)
To find (f-g)(x), we need to subtract the function g(x) from f(x):
(f-g)(x) = f(x) - g(x)
= (-3x^2 - 9x) - (9x + 4)
= -3x^2 - 9x - 9x - 4
= -3x^2 - 18x - 4
The domain of (f-g)(x) is the same as the domain of f(x) and g(x), which is all real numbers. Therefore,
(f-g)(x) = -3x^2 - 18x - 4
d = (-∞, ∞)
To find (fg)(x), we need to multiply f(x) and g(x):
(fg)(x) = f(x) * g(x)
= (-3x^2 - 9x) * (9x + 4)
= -3x^2(9x + 4) - 9x(9x + 4)
= -27x^3 - 12x^2 - 81x^2 - 36x
= -27x^3 - 93x^2 - 36x
The domain of (fg)(x) is the same as the domain of f(x) and g(x), which is all real numbers. Therefore,
(fg)(x) = -27x^3 - 93x^2 - 36x
d = (-∞, ∞)
To find (f/g)(x), we need to divide f(x) by g(x):
(f/g)(x) = f(x) / g(x)
= (-3x^2 - 9x) / (9x + 4)
The domain of (f/g)(x) is the same as the domain of f(x) and g(x), which is all real numbers except for values that make the denominator equal to zero. Therefore, x cannot be -4/9 since it would result in division by zero. So, the domain is:
d = (-∞, -4/9) U (-4/9, ∞)
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)=-3x^2-9x and g(x)=9x+4
(f+g)(x)=
d=
(f-g)(x)=
d=
(fg)(x)=
d=
(f/g)(x)=
d=
1 answer