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 50, Chapter 8: Introductory and Intermediate Algebra for College Students 4th
Uploaded: 2020-06-10T15:49:17-08:00
Duration: 1 min 23 s
Channel: Carl David Cepeda
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 4th

Robert Blitzer 4th Edition

Chapter 8, Problem 50

Instant Answer

Solved by Expert Carl David Cepeda

06/10/2020

Step 1

The first step is to find the value of $g(1)$ from the second table. We can see from the table that $g(1) = 1$. Show more…

Show all steps

Thanks for your feedback!

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

Play audio

Feedback

Carl David Cepeda and 76 other subject Algebra educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

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.

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.

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.

Please give Ace some feedback