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

Ch. 2 - Graphs and Functions

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Lial 13th Edition

Ch. 2 - Graphs and Functions

문제 124

3장, 문제 124

Use the tables for ƒ and g to evaluate each expression.
$open paren f with hook composed with g close paren times 3$

검증된 단계별 안내

Understand that the notation $(ƒ \circ g)(3)$ means $ƒ(g(3))$, which is the composition of the functions $ƒ$ and $g$ evaluated at $3$.

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.

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 $ƒ(g(3))$.

Write the expression clearly as $ƒ(g(3))$ and substitute the values you found from the tables step-by-step.

Conclude by stating that the value of $(ƒ \circ g)(3)$ is the output you found from the $ƒ$ table after substituting $g(3)$.

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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 (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.