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

검증된 단계별 안내

Understand that the expression $ (g \circ f)(-2) $ means $ g(f(-2)) $, which is the composition of functions $ g $ and $ f $ evaluated at $ -2 $.

First, find the value of $ f(-2) $ by looking up $ -2 $ in the table for $ f $ and noting the corresponding output.

Next, take the value you found for $ f(-2) $ and use it as the input for the function $ g $.

Look up this input value in the table for $ g $ to find $ g(f(-2)) $.

The result you get from the table for $ g $ is the value of $ (g \circ f)(-2) $.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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)).

Use the tables for ƒ and g to evaluate each expression.(g∘ƒ)(−2)(g∘ƒ)(-2)