Use the tables for ƒ and g to evaluate each expression.
$(\text{ƒ}\circ g)\left(3\right)$

Verified step by step guidance

1. Understand that the notation \((ƒ \circ g)(3)\) means \(ƒ(g(3))\), which is the composition of the functions \(ƒ\) and \(g\) evaluated at \$3$.
2. First, find the value of \(g(3)\) by looking up the input \$3\( in the table for the function \)g$ and noting the corresponding output.
3. Next, take the output value from \(g(3)\) and use it as the input for the function \(ƒ\). Look up this value in the table for \(ƒ\) to find \(ƒ(g(3))\).
4. Write the expression clearly as \(ƒ(g(3))\) and substitute the values you found from the tables step-by-step.
5. Conclude by stating that the value of \((ƒ \circ g)(3)\) is the output you found from the \(ƒ\) table after substituting \(g(3)\).

Key Concepts

Function Composition

Function composition involves applying one function to the result of another, denoted as (ƒ∘g)(x) = ƒ(g(x)). To evaluate (ƒ∘g)(3), you first find g(3), then use that result as the input for ƒ.

Using Function Tables

Function tables list input-output pairs for functions. To evaluate expressions like ƒ(g(3)), you locate the output of g at 3 in the g-table, then find the corresponding output in the ƒ-table using that value as input.

Evaluating Composite Functions

Evaluating composite functions requires careful step-by-step substitution. After finding g(3), substitute this value into ƒ to get ƒ(g(3)). This process ensures accurate evaluation of nested function expressions.