Question

consider the following functions.
$f(x) = x^3 - 2$ and $g(x) = -2x$
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 given functions

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

Step3: Simplify the expression

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

Step4: Determine the domain

The function $x^3 - 2x - 2$ is a polynomial, which is defined for all real numbers.

Answer:

$(f + g)(x) = x^3 - 2x - 2$
Domain = All real numbers (or $(-\infty, \infty)$)