Question

let \\(f(x) = x^2 + 3x\\) and \\(g(x) = 7x^2 - 2\\). find the function.

\\(f + g\\)

\\((f + g)(x) = \\)

find the domain. (enter your answer using interval notation.)

Explanation:

Define the function sum

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

$$ (f+g)(x) = (x^2 + 3x) + (7x^2 - 2) $$

Simplify the expression

$$ (f+g)(x) = 8x^2 + 3x - 2 $$

Determine the domain

Since \( (f+g)(x) = 8x^2 + 3x - 2 \) is a polynomial function, it is defined for all real numbers.

$$ \text{Domain} = (-\infty, \infty) $$

Answer:

Question 1

Let \( f(x) = x^2 + 3x \) and \( g(x) = 7x^2 - 2 \). Find the function \( f + g \).

\( (f + g)(x) = \) <blank>\(8x^2 + 3x - 2\)</blank>

Question 2

Find the domain. (Enter your answer using interval notation.)

<blank>\((-\infty, \infty)\)</blank>