Question

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

Name: Problem 51, Chapter 2: A Graphical Approach to College Algebra
Uploaded: 2020-07-16T08:17:56-08:00
Duration: 58 s
Channel: Ankit Gupta
Description: Tables for functions f and g are given. Evaluate each expression, if possible. (a) (g ∘f)(1) (b) (f ∘g)(4) (c) (f ∘f)(3) x f(x) x g(x) 1 4 1 2 2 3 2 3 3 1 3 4 4 2 4 5

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

A Graphical Approach to College Algebra

John… 6th Edition

Chapter 2, Problem 51

Instant Answer

Solved by Expert Ankit Gupta

07/16/2020

Step 1

We need to find the values of $(g \circ f)(1)$, $(f \circ g)(4)$, and $(f \circ f)(3)$. Show more…

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

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Key Concepts

Function

A function is a relation that assigns exactly one output value to each input value from its domain. It provides a systematic way to model how one quantity depends on another, serving as a fundamental building block in mathematics.

Input-Output Table

An input-output table is a method of representing a function by listing its inputs alongside their corresponding outputs. This tabular format is especially useful when dealing with discrete functions, allowing one to quickly look up the output for any given input.

Composition of Functions

Function composition is the process of applying one function to the results of another. Specifically, when you have two functions, say f and g, the composition (g ? f)(x) involves first computing f(x) and then applying g to that result. This concept is essential for understanding how multiple transformations or processes combine into a single step.

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