Question

Question was provided via image upload.

Explanation:

Define the function addition rule

Using the Function Addition and Algebra of Functions knowledge points

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

Identify the missing functions

The image shows "Part 1 of 12" asking to find \((f+g)(x)\), but the definitions of \(f(x)\) and \(g(x)\) are cropped out at the top of the screen. To provide a complete and helpful response, we must explain how to perform this operation once the functions are known.

Demonstrate with a standard example

Using the Algebra of Functions knowledge point

$$
LATEXBLOCK0
$$

Answer:

The definitions of the functions \(f(x)\) and \(g(x)\) are cut off at the top of the image.

To find the sum, use the definition:

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

Add the two expressions together and combine like terms. For example, if \(f(x) = x^2 - 3x\) and \(g(x) = 2x + 5\), then:
\((f + g)(x) =\) <blank>\(x^2 - x + 5\)</blank> (Simplify your answer. Do not factor.)