Question

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

Name: Problem 49, Chapter 8: Introductory and Intermediate Algebra for College Students 4th
Uploaded: 2020-06-10T15:45:26-08:00
Duration: 2 min 6 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(10))

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

Introductory and Intermediate Algebra for College Students 4th

Robert Blitzer 4th Edition

Chapter 8, Problem 49

Instant Answer

Solved by Expert Carl David Cepeda

06/10/2020

Step 1

The first step is to evaluate $g(10)$. Looking at the table for $g(x)$, we see that when $x=10$, $g(x)=-1$. So, $g(10)=-1$. Show more…

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

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Key Concepts

Function Composition

This concept involves applying one function to the result of another. In a composite function, the output of one function becomes the input of the next. This requires evaluating the inner function first and then applying the outer function to that output.

Function Tables

Function tables provide a way to represent functions by listing pairs of inputs and outputs. They are particularly useful for evaluating functions and their compositions, as you can directly look up the function value associated with a particular input.

Inverse Functions

An inverse function reverses the effect of the original function, mapping outputs back to their original inputs. When evaluating expressions like f?¹(g(10)), you first compute g(10) and then find the value in the domain of f that corresponds to that output, effectively 'undoing' f.

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