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.

Question

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=

Answer 1

To find (f+g)(x), we need to add the two given functions together:
(f+g)(x) = f(x) + g(x) = (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), which is all real numbers. So, the domain is (-∞, ∞).

To find (f-g)(x), we need to subtract g(x) from f(x):
(f-g)(x) = f(x) - g(x) = (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. So, the domain is (-∞, ∞).

To find (fg)(x), we need to multiply the two given functions together:
(fg)(x) = f(x) * g(x) = (3x^2-9x) * (9x+4) = 27x^3 -3x^2 - 36x^2 - 36x

The domain of (fg)(x) is the same as the domain of f(x) and g(x), which is all real numbers. So, the domain is (-∞, ∞).

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 all real numbers except for any values of x that make the denominator equal to zero. Setting the denominator equal to zero, we solve:
9x + 4 = 0
9x = -4
x = -4/9

So, the domain of (f/g)(x) is (-∞, -4/9) U (-4/9, ∞).