Question

consider the following functions.\\( f(x) = -2x \\) and \\( g(x) = x - 3 \\)\
step 1 of 2: find the formula for \\( (f + g)(x) \\) and simplify your answer. then find the domain for \\( (f + g)(x) \\). round your answer to two decimal places, if necessary.\
\\( (f + g)(x) = \\)\
domain =

Explanation:

Step1: Define sum of functions

$(f+g)(x) = f(x) + g(x)$

Step2: Substitute function formulas

$(f+g)(x) = -2x + (x - 3)$

Step3: Simplify the expression

$(f+g)(x) = -2x + x - 3 = -x - 3$

Step4: Determine the domain

Both $f(x)$ and $g(x)$ are linear functions, defined for all real numbers. The domain of $(f+g)(x)$ is the intersection of the domains of $f(x)$ and $g(x)$.

Answer:

$(f + g)(x) = -x - 3$
Domain = All real numbers (or $(-\infty, \infty)$)