Question

Use the tables of values of $f$ and $g$ to answer each problem. $$\begin{array}{|c|c|}\hline x & f(x) \\\hline 2 & 4 \\\hline 4 & 9 \\\hline 6 & 13 \\\hline 13 & 17 \\ \hline\end{array}$$ $$\begin{array}{|c|c|}\hline x & g(x) \\\hline 0 & 0 \\\hline 2 & 4 \\\hline 3 & 9 \\\hline 4 & 16 \\ \hline\end{array}$$ $$(g \circ f)(2)$$

Name: Problem 90, Chapter 3: College Algebra
Uploaded: 2020-07-07T08:40:54-08:00
Duration: 14 s
Channel: Amy Jiang
Description: Use the tables of values of f and g to answer each problem. x f(x) 2 4 4 9 6 13 13 17 x g(x) 0 0 2 4 3 9 4 16 (g ∘f)(2)

   Use the tables of values of $f$ and $g$ to answer each problem.
$$\begin{array}{|c|c|}\hline x & f(x) \\\hline 2 & 4 \\\hline 4 & 9 \\\hline 6 & 13 \\\hline 13 & 17 \\
\hline\end{array}$$
$$\begin{array}{|c|c|}\hline x & g(x) \\\hline 0 & 0 \\\hline 2 & 4 \\\hline 3 & 9 \\\hline 4 & 16 \\
\hline\end{array}$$
$$(g \circ f)(2)$$

College Algebra

R. David Gustafson,… 11th Edition

Chapter 3, Problem 90

Instant Answer

Solved by Expert Amy Jiang

07/07/2020

Step 1

This means we first apply the function $f$ to the input 2, and then apply the function $g$ to the result. Show more…

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Use the tables of values of $f$ and $g$ to answer each problem. $$\begin{array}{|c|c|}\hline x & f(x) \\\hline 2 & 4 \\\hline 4 & 9 \\\hline 6 & 13 \\\hline 13 & 17 \\ \hline\end{array}$$ $$\begin{array}{|c|c|}\hline x & g(x) \\\hline 0 & 0 \\\hline 2 & 4 \\\hline 3 & 9 \\\hline 4 & 16 \\ \hline\end{array}$$ $$(g \circ f)(2)$$

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Key Concepts

Function Notation

Function notation is a concise way to represent functions, using expressions like f(x) to denote the output of function f when given an input x. This notation is fundamental in understanding operations like mapping an input to an output and composing functions.

Function Composition

Function composition involves applying one function to the results of another. In mathematical notation, (f ? g)(x) means that you first compute g(x) and then apply the function f to that result. This concept is central when combining multiple transformations or operations on input values.

Interpreting Function Tables

Function tables present discrete pairs of inputs and corresponding outputs for a function. They are used to quickly look up the value of a function at a specific input, which is especially useful when evaluating compositions of functions by first finding the output of one function and then using that as the input for another function.

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