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Substitution is a common technique in mathematics where you replace a variable with a given value. It's like a replacement method. For example, in the exercise, we are given a function \( f(x) = \frac{x + 2}{x - 1} \) and are asked to find \( f(2) \). To do this, we substitute the value 2 for x in the function. This step converts the general expression into a specific one.

Substitution helps you transform an abstract equation into a solvable problem. It's often the first step in evaluating functions. Always ensure you replace every instance of the variable in the function.

Simplification is the process of reducing an expression to its most basic form. After substitution, simplification makes the problem more manageable. In the problem, once we substitute 2 into the function, we get \( \frac{2 + 2}{2 - 1} \).

Simplification involves carrying out the arithmetic operations inside the expression. Here, \( 2 + 2 = 4 \) and \( 2 - 1 = 1 \). Thus, the expression becomes \( \frac{4}{1} \), which simplifies further to 4.

Remember, the goal of simplification is to make the expression as clear and straightforward as possible.

Function notation is a way of representing functions in a compact form. It uses the format \( f(x) \), where 'f' signifies the function name, and 'x' represents the input value or variable. The expression \( f(x) = \frac{x + 2}{x - 1} \) shows how 'x' is transformed within the function.

When you see something like \( f(2) \), it indicates that you need to substitute 2 into the function for 'x'. Function notation helps clearly identify and evaluate functions by specifying both the operation and the input value.

It's essential to understand this notation because it is widely used in different areas of mathematics, including algebra and calculus. Always pay attention to what value is being substituted for the variable in function notation.