I really am trying to work these problems out on my own. Please help
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-x-6
x is all real numbers and x is not equal to -6
(f x g) (x) (f/g) (x) 3x^2/6-x
18x^3-x
x is all real numbers
(f/g)(x) 3x^2/ 1/6+x
x is all real numbers; x is not equal to 6
Sure! I'd be happy to help you work through these problems.
1) (f+g)(x): To find the sum of two functions, f(x) and g(x), you simply add their values for each x. So for this problem, you would add 3x^2 and 1/6+x.
Answer: (f+g)(x) = 3x^2 + (1/6+x)
Domain: The domain refers to the set of all possible x-values for which the function is defined. In this case, since we're adding two polynomial functions, the domain will be all real numbers, except any values of x that would make the denominator (if there are any) equal to zero.
In this case, there are no denominators involved, so the domain is all real numbers.
2) (f-g)(x): To find the difference between two functions, f(x) and g(x), you subtract their values for each x. So for this problem, you would subtract 1/6+x from 3x^2.
Answer: (f-g)(x) = 3x^2 - (1/6+x)
Domain: Similarly to the previous problem, the domain for the difference of two polynomial functions is all real numbers, except any values of x that would make the denominator (if there are any) equal to zero.
In this case, there are no denominators involved, so the domain is all real numbers.
3) (f x g)(x): The notation (f x g)(x) represents the composition of two functions, f(x) and g(x), which means you substitute the entire expression of g(x) into f(x). So for this problem, you would substitute 1/6+x into 3x^2.
Answer: (f x g)(x) = 3(1/6+x)^2
Simplifying further, (f x g)(x) = 3(1/36 + 2/6x + x^2) = 3/36 + 6/6x + 3x^2 = 1/12 + x/2 + 3x^2
Domain: Since both functions involved are polynomial functions, the domain is all real numbers.
4) (f/g)(x): To find the quotient of two functions, f(x) and g(x), you divide f(x) by g(x). So for this problem, you would divide 3x^2 by 1/6+x.
Answer: (f/g)(x) = (3x^2) / (1/6+x)
To simplify the division, you multiply 3x^2 by the reciprocal of (1/6+x):
(f/g)(x) = (3x^2) * [(6+x)/1]
(f/g)(x) = 3x^2 * (6+x) = 18x^3 + 3x^2
Domain: Similar to previous problems, the domain for the quotient of two polynomial functions is all real numbers, except any values of x that would make the denominator (if there are any) equal to zero.
In this case, the denominator is 1/6+x. To avoid division by zero, x cannot be equal to -6.
So, the domain is x is all real numbers except x = -6.