Evaluate each function at the given values of the independent variable and simplify. (a) f(-2), (b) f(1), (c) f(2)

Verified step by step guidance

1. Step 1: Understand the problem. You are given a function f(x) and need to evaluate it at specific values of the independent variable x: -2, 1, and 2. This means substituting these values into the function and simplifying the resulting expressions.
2. Step 2: Substitute x = -2 into the function f(x). Replace every occurrence of x in the function with -2, and simplify the resulting expression.
3. Step 3: Substitute x = 1 into the function f(x). Replace every occurrence of x in the function with 1, and simplify the resulting expression.
4. Step 4: Substitute x = 2 into the function f(x). Replace every occurrence of x in the function with 2, and simplify the resulting expression.
5. Step 5: Write down the simplified results for f(-2), f(1), and f(2). These are the evaluated values of the function at the given points.

Key Concepts

Function Evaluation

Function evaluation involves substituting a specific value for the independent variable in a function. For example, if f(x) = x^2, evaluating f(2) means calculating 2^2, which equals 4. This process is fundamental in understanding how functions behave at different points.

Independent Variable

The independent variable is the input of a function, typically represented by 'x' in mathematical expressions. It is the variable that you can control or change, and its value determines the output of the function. In the question, -2, 1, and 2 are the values of the independent variable for which the function is evaluated.

Simplification

Simplification is the process of reducing an expression to its simplest form. This may involve combining like terms, factoring, or reducing fractions. After evaluating the function at the specified values, simplifying the results ensures clarity and conciseness in the final answer.