Use the tables for ƒ and g to evaluate each expression. (ƒ∘g)(3)

Verified step by step guidance

1. Identify the function g at the input 3, which is denoted as g(3).
2. Find the value of g(3) from the table provided for g.
3. Use the value obtained from g(3) as the input for the function ƒ, which is denoted as ƒ(g(3)).
4. Find the value of ƒ at the input g(3) from the table provided for ƒ.
5. The value of ƒ(g(3)) is the result of the composition (ƒ∘g)(3).

Key Concepts

Function Composition

Function composition is the process of combining two functions, where the output of one function becomes the input of another. In this case, (ƒ∘g)(3) means you first evaluate g at 3, and then use that result as the input for the function ƒ. Understanding this concept is crucial for correctly evaluating the expression.

Evaluating Functions

Evaluating a function involves substituting a specific value into the function's formula or table to find the corresponding output. For example, if g(3) is given in a table, you would look up the value associated with 3 to find the output of g. This step is essential for function composition, as it determines the input for the next function.

Function Notation

Function notation, such as ƒ(x) or g(x), is a way to represent functions and their outputs based on inputs. It allows for clear communication of which function is being used and what the input values are. Familiarity with function notation is important for understanding how to manipulate and evaluate functions in expressions like (ƒ∘g)(3).