Question

Use the table to evaluate each expression. $$ \begin{array}{|c|c|c|c|c|c|c|} \hline x & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline f(x) & 3 & 1 & 5 & 6 & 2 & 4 \\ \hline g(x) & 5 & 3 & 4 & 1 & 3 & 2 \\ \hline \end{array} $$ (a) $g(g(g(2)))$ (b) $(f \circ f \circ f)(1)$ (c) $(f \circ f \circ g)(1)$ (d) $(g \circ f \circ g)(3)$

Name: Problem 56, Chapter 1: Calculus: Early Transcendentals, Metric Edition
Uploaded: 2022-09-12T19:08:46-08:00
Channel: Carson Merrill
Description: Use the table to evaluate each expression. x 1 2 3 4 5 6 f(x) 3 1 5 6 2 4 g(x) 5 3 4 1 3 2 (a) g(g(g(2))) (b) (f ∘f ∘f)(1) (c) (f ∘f ∘g)(1) (d) (g ∘f ∘g)(3)

   Use the table to evaluate each expression. 
$$
\begin{array}{|c|c|c|c|c|c|c|}
\hline x & 1 & 2 & 3 & 4 & 5 & 6 \\
\hline f(x) & 3 & 1 & 5 & 6 & 2 & 4 \\
\hline g(x) & 5 & 3 & 4 & 1 & 3 & 2 \\
\hline
\end{array}
$$ 
(a) $g(g(g(2)))$
(b) $(f \circ f \circ f)(1)$
(c) $(f \circ f \circ g)(1)$
(d) $(g \circ f \circ g)(3)$

Calculus: Early Transcendentals, Metric Edition

James Stewart,… 9th Edition

Chapter 1, Problem 56

Instant Answer

Solved by Expert Carson Merrill

09/12/2022

Step 1

So the expression becomes $g(g(3))$. Show more…

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Use the table to evaluate each expression. $$ \begin{array}{|c|c|c|c|c|c|c|} \hline x & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline f(x) & 3 & 1 & 5 & 6 & 2 & 4 \\ \hline g(x) & 5 & 3 & 4 & 1 & 3 & 2 \\ \hline \end{array} $$ (a) $g(g(g(2)))$ (b) $(f \circ f \circ f)(1)$ (c) $(f \circ f \circ g)(1)$ (d) $(g \circ f \circ g)(3)$

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Key Concepts

Function Table Evaluation

This concept involves using a provided table that lists input-output pairs for a function. The table allows one to quickly look up the output associated with a given input, which is essential for evaluating functions in problems where the function is defined by specific discrete values.

Composite Functions

Composite functions are created by applying one function to the results of another. The expression (f ? g)(x) means that function g is applied to x first, and then function f is applied to the result. Understanding composite functions is crucial for breaking down complex evaluations into simpler, sequential steps.

Order of Evaluation in Function Composition

When dealing with nested function compositions, it is important to work from the innermost function to the outermost function. This ensures that each part of the composite function is properly computed in sequence, with the output of one function becoming the input for the next.

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