If f(x)=3x^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) (3x^2) - (1/6+x) 3x^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) 3x^2/6-x x is all real numbers and x is not equal to 6
To find the values and domains of the given functions, we need to perform the specified operations and apply the given restrictions.
1. (f+g)(x) = (3x^2) + (1/6+x)
To find the sum, we simply combine like terms:
(f+g)(x) = 3x^2 + (1/6) + x
The domain of (f+g)(x) is all real numbers except x = 6. This is because the expression 1/6+x results in division by zero when x equals 6.
2. (f-g)(x) = (3x^2) - (1/6+x)
To find the difference, we subtract the second function from the first:
(f-g)(x) = 3x^2 - (1/6) - x
= 3x^2 - x - (1/6)
The domain of (f-g)(x) is all real numbers except x = -6. This is because the expression 1/6+x results in division by zero when x equals -6.
3. (f x g)(x)
The notation (f x g)(x) represents function composition, or applying one function to the output of another. To find this value, we substitute g(x) into f(x).
f(x) = 3x^2
g(x) = 1/6 + x
(f x g)(x) = f(g(x)) = f(1/6 + x)
Substitute g(x) into f(x):
= 3(1/6 + x)^2
Simplifying further requires expanding the expression and manipulating the terms.
4. (f/g)(x) = (3x^2)/(6-x)
To find the quotient, we divide the first function by the second:
(f/g)(x) = (3x^2)/(6-x)
The domain of (f/g)(x) is all real numbers except x = 6. This is because the expression 6 - x results in division by zero when x equals 6.