If f(x)=3^2 g(x)= 1/6+x find the following and give the domain
(f+g) (x) (3x^2) + (1/6+x) x is all real numbers and x is not equal to 6
(f-g) (x) (3^2) - (1/6+x) 3^2 -6-x x is all real numbers and x is not equal to -6
(f x g) (x) I do not understand
(f/g) (x) 3^2/6-x x is all real numbers and x is not equal to 6
To find the values and domain of the given functions, we will substitute the given expressions for f(x) and g(x) into the equations and simplify as needed.
1. (f+g)(x) = (3^2) + (1/6+x) = 9 + (1/6+x) = 9 + 1/6 + x = 9 + 1/6 + x
Domain: Since x can be any real number except 6, the domain is all real numbers except x=6.
2. (f-g)(x) = (3^2) - (1/6+x) = 9 - (1/6+x) = 9 - 1/6 - x = 9 - 1/6 - x
Domain: x can be any real number except -6, so the domain is all real numbers except x=-6.
3. (f x g)(x) means the product of f(x) and g(x). To find it, we multiply the expressions for f(x) and g(x):
(f x g)(x) = (3^2) x (1/6+x) = 9 x (1/6+x) = 9/6 + 9x/6 = 3/2 + 3x/2
Domain: There are no restrictions for the domain, so it is all real numbers.
4. (f/g)(x) = (3^2) / (6-x) = 9 / (6-x)
Domain: Note that the denominator cannot be zero, so 6-x cannot be equal to zero, i.e., x ≠ 6. Therefore, the domain is all real numbers except x=6.
To summarize:
1. (f+g)(x) = 9 + 1/6 + x, domain: all real numbers except x=6.
2. (f-g)(x) = 9 - 1/6 - x, domain: all real numbers except x=-6.
3. (f x g)(x) = 3/2 + 3x/2, domain: all real numbers.
4. (f/g)(x) = 9 / (6-x), domain: all real numbers except x=6.
To find (f+g)(x), we add f(x) and g(x) together:
(f+g)(x) = f(x) + g(x)
(f+g)(x) = 3^2 + (1/6+x)
(f+g)(x) = 9 + (1/6+x)
The domain for (f+g)(x) is all real numbers, except x cannot be equal to 6 (since division by zero is undefined).
To find (f-g)(x), we subtract g(x) from f(x):
(f-g)(x) = f(x) - g(x)
(f-g)(x) = 3^2 - (1/6+x)
(f-g)(x) = 9 - (1/6+x)
(f-g)(x) = 9 - 1/(6+x)
The domain for (f-g)(x) is all real numbers, except x cannot be equal to -6 (since division by zero is undefined).
To find (f x g)(x), we multiply f(x) by g(x):
(f x g)(x) = f(x) * g(x)
(f x g)(x) = 3^2 * (1/6+x)
(f x g)(x) = 9 * (1/6+x)
(f x g)(x) = 9/1 * (1/6+x)
The domain for (f x g)(x) is all real numbers.
To find (f/g)(x), we divide f(x) by g(x):
(f/g)(x) = f(x) / g(x)
(f/g)(x) = (3^2) / (1/6+x)
(f/g)(x) = 9 / (1/6+x)
The domain for (f/g)(x) is all real numbers, except x cannot be equal to 6 (since division by zero is undefined).