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Function addition is the process of adding two functions together. We'll use the given functions to form a new function. The key idea is to simply add their corresponding outputs. Given functions like and , their addition is defined as which means that we add each output of to the corresponding output of . Regularly practicing function addition will help ease you into more complex operations. In our example, this looks like: after substituting the given functions. Once you get comfortable, you'll be ready to move on to other operations, such as subtraction and multiplication of functions.

Understanding algebraic expressions is key for performing function operations. An algebraic expression is a mathematical phrase that can contain numbers, variables, and operations like addition or multiplication. In our example, and are algebraic expressions. These expressions combine numbers and variables (like ) using arithmetic operations. To combine these expressions, you must follow the appropriate algebraic rules.

Remember, expressions can be simplified to make calculations easier. When simplifying, it's essential to combine like terms and handle fractions properly. For example, in the problem: , you leave it unsimplified or combine terms if possible. Simplification helps in evaluating these expressions at any given value of .

Composite functions involve combining two functions using composition rather than addition. The notation for a composite function is which means apply first and then apply the result to .

Though not required in this exercise, understanding composites helps deepen your grasp of function operations. Let’s consider our example: and . A composite function, like , would mean evaluating first and then plugging this result into .

• If and , then compute where .
• So, evaluate and then use this result in .

This way, composite functions build new functions based on the outputs of others, which is crucial for advanced math topics like calculus.