Question

Let f(x)= 2x^2+x-3 and g(x)=x-1. Perform the function operation and then find the domain. (f+g)(x)

Answer 1

All real numbers

Explanation:

The function operation of adding two functions f(x) and g(x) is defined as (f+g)(x) = f(x) + g(x).

Given f(x)= 2x^2+x-3 and g(x)=x-1, we have:

(f+g)(x) = f(x) + g(x) = (2x^2+x-3) + (x-1) = 2x^2+2x-4

The domain of a function is the set of all possible input values (x-values) for which the function produces a valid output (y-value). Since the function (f+g)(x) = 2x^2+2x-4 is a polynomial function, it is defined for all real values of x. Therefore, the domain of (f+g)(x) is all real numbers, or (-infinity,+infinity)