Question

Let f(x)=2x^(2)+x,g(x)=x^(2)+2x+6, and h(x)=(x+2)/(x-4). Perform the indicated operation and state the domain. (4 pts ) (f+g)(x)

Answer 1

To find (f+g)(x), add the functions f(x) = 2x^2 + x and g(x) = x^2 + 2x + 6 to get (f+g)(x) = 3x^2 + 3x + 6. The domain of (f+g)(x) is all real numbers, expressed as (-∞, ∞).

Step-by-step explanation:

Performing the Operation (f+g)(x)

To operate (f+g)(x), we need to add the functions f(x) and g(x) together. Given that f(x) = 2x2 + x and g(x) = x2 + 2x + 6, we combine like terms to find the sum:

(f+g)(x) = f(x) + g(x) = (2x2 + x) + (x2 + 2x + 6)

This simplifies to:

(f+g)(x) = 3x2 + 3x + 6

The domain of the sum is the set of all real numbers for which both f(x) and g(x) are defined. Since both f(x) and g(x) are polynomials, they are defined for all real numbers, so the domain of (f+g)(x) is all real numbers, expressed as (-∞, ∞).