To find each of the following and their respective domains, we will evaluate the given functions as indicated:
1) (f+g)(x) = f(x) + g(x)
= (4/x) + (x+9)
= 4/x + x + 9
Therefore, (f+g)(x) = 4/x + x + 9
Domain (d): The domain of (f+g)(x) is all real numbers except for x = 0 (since the function f(x) = 4/x has a denominator of x).
Domain: (-∞, 0) ∪ (0, ∞)
2) (f-g)(x) = f(x) - g(x)
= (4/x) - (x+9)
= 4/x - x - 9
Therefore, (f-g)(x) = 4/x - x - 9
Domain (d): The domain of (f-g)(x) is all real numbers except for x = 0 (since the function f(x) = 4/x has a denominator of x).
Domain: (-∞, 0) ∪ (0, ∞)
3) (fg)(x) = f(x) * g(x)
= (4/x) * (x+9)
= 4(x+9)/x
Therefore, (fg)(x) = 4(x+9)/x
Domain (d): The domain of (fg)(x) is all real numbers except for x = 0 (since the function f(x) = 4/x has a denominator of x).
Domain: (-∞, 0) ∪ (0, ∞)
4) (f/g)(x) = f(x) / g(x)
= (4/x) / (x+9)
= 4 / (x(x+9))
Therefore, (f/g)(x) = 4 / (x(x+9))
Domain (d): The domain of (f/g)(x) is all real numbers except for x = 0 and x = -9 (since the functions f(x) = 4/x and g(x) = x+9 both have a denominator of x and x+9, respectively).
Domain: (-∞, -9) ∪ (-9, 0) ∪ (0, ∞)
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)=4/x and g(x)=x+9
(f+g)(x)=
d=
(f-g)(x)=
d=
(fg)(x)=
d=
(f/g)(x)=
d=
1 answer