Question

f and g are defined by the following tables. Use the tables to evaluate each composite function. $$\begin{array}{c|c} \hline x & f(x) \\ \hline-1 & 1 \\ \hline 0 & 4 \\ \hline 1 & 5 \\ \hline 2 & -1 \\ \hline \end{array}$$ $$\begin{array}{c|c} \hline x & g(x) \\ \hline-1 & 0 \\ \hline 1 & 1 \\ \hline 4 & 2 \\ \hline 10 & -1 \\ \hline \end{array}$$ $f^{-1}(g(1))$

Name: Problem 60, Chapter 9: Introductory and Intermediate Algebra for College Students
Uploaded: 2020-07-28T21:38:52-08:00
Duration: 27 s
Channel: James Kiss
Description: f and g are defined by the following tables. Use the tables to evaluate each composite function. x f(x) -1 1 0 4 1 5 2 -1 x g(x) -1 0 1 1 4 2 10 -1 f^-1(g(1))

   f and g are defined by the following tables.
Use the tables to evaluate each composite function.
$$\begin{array}{c|c}
\hline x & f(x) \\
\hline-1 & 1 \\
\hline 0 & 4 \\
\hline 1 & 5 \\
\hline 2 & -1 \\
\hline
\end{array}$$

$$\begin{array}{c|c}
\hline x & g(x) \\
\hline-1 & 0 \\
\hline 1 & 1 \\
\hline 4 & 2 \\
\hline 10 & -1 \\
\hline
\end{array}$$
 $f^{-1}(g(1))$

Introductory and Intermediate Algebra for College Students

Robert Blitzer 6th Edition

Chapter 9, Problem 60

Instant Answer

Solved by Expert James Kiss

07/28/2020

Step 1

Looking at the table for g(x), we see that when x = 1, g(x) = 1. So, g(1) = 1. Show more…

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f and g are defined by the following tables. Use the tables to evaluate each composite function. $$\begin{array}{c|c} \hline x & f(x) \\ \hline-1 & 1 \\ \hline 0 & 4 \\ \hline 1 & 5 \\ \hline 2 & -1 \\ \hline \end{array}$$ $$\begin{array}{c|c} \hline x & g(x) \\ \hline-1 & 0 \\ \hline 1 & 1 \\ \hline 4 & 2 \\ \hline 10 & -1 \\ \hline \end{array}$$ $f^{-1}(g(1))$

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Key Concepts

Composite Functions

Composite functions involve applying one function to the result of another. This concept requires first evaluating the inner function and then using that result as the input for the outer function, reflecting the idea of function composition.

Inverse Functions

An inverse function reverses the process of the original function. Given a function f, its inverse f?¹ produces the input that was mapped to a given output by f. This is crucial when finding a value that originally led to a specific function output.

Tabular Function Evaluation

Functions are often represented in tables, where input-output pairs are listed explicitly. Skills in reading and interpreting these tables allow one to accurately retrieve function values, which is essential when evaluating composite or inverse functions.

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