Question

Tables for finctions $f$ and $g$ are given. Evaluate cach expression, if possible. (a) $(g \circ f)(1)$(b) $(f \circ g)(4)$(c) $(f \circ f)(3)$ $$\begin{array}{c|c}x & f(x) \\1 & 4 \\2 & 3 \\3 & 1 \\4 & 2\end{array}\quad\quad\quad \begin{array}{c|c}x & g(x) \\1 & 2 \\2 & 3 \\3 & 4 \\4 & 5\end{array}$$

Name: Problem 43, Chapter 2: A Graphical Approach to Precalculus with Limits
Uploaded: 2020-08-16T22:45:14-08:00
Duration: 1 min 2 s
Channel: Amy Jiang
Description: Tables for finctions f and g are given. Evaluate cach expression, if possible. (a) (g ∘f)(1)(b) (f ∘g)(4)(c) (f ∘f)(3) x f(x) 1 4 2 3 3 1 4 2 x g(x) 1 2 2 3 3 4 4 5

   Tables for finctions $f$ and $g$ are given. Evaluate cach expression, if possible.
(a) $(g \circ f)(1)$(b) $(f \circ g)(4)$(c) $(f \circ f)(3)$
$$\begin{array}{c|c}x & f(x) \\1 & 4 \\2 & 3 \\3 & 1 \\4 & 2\end{array}\quad\quad\quad
\begin{array}{c|c}x & g(x) \\1 & 2 \\2 & 3 \\3 & 4 \\4 & 5\end{array}$$

A Graphical Approach to Precalculus with Limits

John Hornsby,… 7th Edition

Chapter 2, Problem 43

Instant Answer

Solved by Expert Amy Jiang

08/16/2020

Step 1

This means we first apply the function $f$ to $1$, and then apply the function $g$ to the result. Looking at the table for $f$, we see that $f(1) = 4$. Show more…

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Tables for finctions $f$ and $g$ are given. Evaluate cach expression, if possible. (a) $(g \circ f)(1)$(b) $(f \circ g)(4)$(c) $(f \circ f)(3)$ $$\begin{array}{c|c}x & f(x) \\1 & 4 \\2 & 3 \\3 & 1 \\4 & 2\end{array}\quad\quad\quad \begin{array}{c|c}x & g(x) \\1 & 2 \\2 & 3 \\3 & 4 \\4 & 5\end{array}$$

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Key Concepts

Evaluating Functions Using Lookup Tables

Lookup tables provide a structured way to evaluate functions by listing input values alongside their corresponding outputs. When given a table, you can find the function's value at a particular point by locating the input and reading off the associated output. This method is particularly useful for discrete functions or when the function is defined only by specific input-output pairs, and it is essential for accurately computing composite functions via table evaluations.

Function Composition

Function composition involves applying one function to the result of another, following the notation (g ? f)(x) = g(f(x)). This concept requires first evaluating the inner function and then using its output as the input for the outer function, making the order of operations crucial. It is a foundational idea in algebra and calculus that emphasizes how functions can be combined to form new functions.

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