Question

let $f(x) = 2x^2 + x - 11$ and $g(x) = x - 1$. perform the function operation and then find the domain.
$(f + g)(x)$

$(f + g)(x) = 2x^2 + 2x - 12$ (simplify your answer.)
what is the domain of $(f + g)(x)$?

a. the domain of $f + g$ is the set of all real numbers.

b. the domain of $f + g$ is the set of all $x \leq 0$.

c. the domain of $f + g$ is the set of all real numbers except $x = 0$.

d. the domain of $f + g$ is the set of all $x \geq 0$.

Explanation:

Step1: Analyze the function type

The function \((f + g)(x)=2x^{2}+2x - 12\) is a polynomial function.

Step2: Recall the domain of polynomial functions

For any polynomial function (in the form of \(a_{n}x^{n}+a_{n - 1}x^{n-1}+\cdots+a_{1}x + a_{0}\), where \(n\) is a non - negative integer and \(a_{i}\) are real numbers), there are no restrictions on the input values of \(x\) (no division by zero, no square roots of negative numbers in the real - number system for the domain consideration here). So the domain of a polynomial function is the set of all real numbers.

Answer:

A. The domain of \(f + g\) is the set of all real numbers.