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Function composition involves combining two functions where the output of one function becomes the input of the other. For example, if you have functions \(f(x)\) and \(g(x)\), their composition is denoted as \(f(g(x))\). This means you first apply \(g(x)\) to the input and then apply \(f(x)\) to the result. It is important to note that the order in which you compose the functions matters.\(
\) One common mistake is to think that \(f(g(x))\) is the same as \(g(f(x))\), but this is not true. \(
\) Here's a quick example to illustrate: if \(f(x) = 2x + 1\) and \(g(x) = x^2\), then \(f(g(x)) = 2(x^2) + 1 = 2x^2 + 1\), while \(g(f(x)) = (2x + 1)^2 = 4x^2 + 4x + 1\).\(
\) In this exercise, while we are not directly composing functions, understanding composition can help you see how different functions interact and how their outputs can influence further calculations.

Substitution is a fundamental concept where you replace a variable with a specific value. In this exercise, we substitute \(-4\) into the given functions \(f(x)\) and \(g(x)\). This is how you evaluate a function at a specific value.\(
\) For instance, for \(f(x) = -2x + 3\), substituting \(x = -4\) gives: \( f(-4) = -2(-4) + 3 = 8 + 3 = 11\). Here, the variable \(x\) is replaced by \(-4\).\(
\) Similarly, for \(g(x) = x^2 - 5\), substituting \(x = -4\) results in: \( g(-4) = (-4)^2 - 5 = 16 - 5 = 11\). Substitution is essential for evaluating and understanding the behavior of functions at specific points.\(
\) It also prepares us for more complex topics where we might need to substitute not just numbers but even other expressions or variables.

Algebraic expressions are combinations of variables, numbers, and operations (like addition, subtraction, multiplication, and division). Understanding these expressions is crucial for solving many math problems, including evaluating functions.\(
\) Take the function \(f(x) = -2x + 3\) as an example. This is an algebraic expression where \(-2x + 3\) tells us that we need to multiply the input \(x\) by \(-2\) and then add \(3\).\(
\) Similarly, for \(g(x) = x^2 - 5\), the expression \(x^2 - 5\) instructs us to square the input \(x\) and then subtract \(5\). Understanding how to manipulate these expressions is fundamental for algebra.\(
\) In the step-by-step solution, we used these expressions to find \(f(-4)\) and \(g(-4)\). This involves basic arithmetic operations within the algebraic structure defined by the functions.