Use the tables for ƒ and g to evaluate each expression.
$(g\circ \text{ƒ})(-2)$

Verified step by step guidance

1. Understand that the expression \( (g \circ f)(-2) \) means \( g(f(-2)) \), which is the composition of functions \( g \) and \( f \) evaluated at \( -2 \).
2. First, find the value of \( f(-2) \) by looking up \( -2 \) in the table for \( f \) and noting the corresponding output.
3. Next, take the value you found for \( f(-2) \) and use it as the input for the function \( g \).
4. Look up this input value in the table for \( g \) to find \( g(f(-2)) \).
5. The result you get from the table for \( g \) is the value of \( (g \circ f)(-2) \).

Key Concepts

Function Composition

Function composition involves applying one function to the result of another, denoted as (g∘ƒ)(x) = g(ƒ(x)). To evaluate (g∘ƒ)(-2), first find ƒ(-2), then use that output as the input for g.

Using Function Tables

Function tables list input-output pairs for functions. To evaluate a function at a specific input, locate the input value in the table and read off the corresponding output value.

Order of Operations in Composition

When evaluating (g∘ƒ)(x), the order matters: compute ƒ(x) first, then apply g to that result. This ensures correct evaluation and avoids confusion between g(ƒ(x)) and ƒ(g(x)).