Use the table to evaluate each expression, if possible. (f-g)(3)

Verified step by step guidance

1. <insert step 1> Identify the functions f(x) and g(x) from the table.>
2. <insert step 2> Find the values of f(3) and g(3) from the table.>
3. <insert step 3> Use the formula for (f-g)(x) = f(x) - g(x) to set up the expression (f-g)(3) = f(3) - g(3).>
4. <insert step 4> Substitute the values of f(3) and g(3) into the expression.>
5. <insert step 5> Simplify the expression to find the result of (f-g)(3).>

Key Concepts

Function Evaluation

Function evaluation involves substituting a specific input value into a function to determine its output. In this case, evaluating (f-g)(3) requires calculating the difference between the values of functions f and g at the input of 3. Understanding how to evaluate functions is crucial for solving problems that involve operations on functions.

Operations on Functions

Operations on functions include addition, subtraction, multiplication, and division of two or more functions. The expression (f-g)(x) represents the subtraction of function g from function f. Mastery of these operations is essential for manipulating and combining functions to find new outputs based on existing ones.

Function Notation

Function notation is a way to represent functions and their outputs clearly. For example, f(x) denotes the output of function f for input x. Understanding function notation is vital for interpreting expressions like (f-g)(3), as it clarifies which functions are being used and how they relate to each other.