91Ó°ÊÓ

Substitution is a crucial concept in algebra, especially when dealing with functions. It involves replacing a variable with a specific value to evaluate the function. In this exercise, we were given a function, and we needed to find its value at a particular point. To do this, we substituted the given value into the function. Let's break it down step-by-step.
First, identify the function. Here, we had two functions: \(f(x) = -3x + 4\) and \(g(x) = -x^2 + 4x + 1\). We were asked to find \(g(3)\), which means we replace every \(x\) in \(g(x)\) with 3.

• Write the function: \(g(x) = -x^2 + 4x + 1\)
• Substitute 3 for \(x\): \(g(3) = -(3)^2 + 4(3) + 1\)

This simple act of replacing \(x\) with 3 helps us proceed to the next steps where we perform the arithmetic operations to simplify and find the function's value at \(x = 3\).
Substitution is not just limited to numbers. It can also be used with expressions to simplify complex equations. Understanding this concept is vital as it lays the foundation for solving more advanced algebraic problems.

Function notation is a way of representing functions in a concise manner. Instead of writing expressions every time, functions use notation like \(f(x)\) or \(g(x)\). In our exercise, \(f(x)\) and \(g(x)\) represent two different functions.
Function notation helps to identify the function being used and the variable involved. For example, in \(g(x) = -x^2 + 4x + 1\), \(g\) is the name of the function, and \(x\) is the variable. When we want to find the value of the function at a specific point, say \(x = 3\), we use notation like \(g(3)\).
Some key points about function notation:

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