/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 104 If equations for \(f\) and \(g\)... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 104

If equations for \(f\) and \(g\) are given, explain how to find \(f-g .\)

Short Answer

Expert verified
The difference between function \(f\) and function \(g\), represented as \(f - g\), is obtained by subtracting the equation for \(g\) from that for \(f\). If the functions are \(f(x) = ax + b\) and \(g(x) = cx + d\), then \(f - g = (a-c)x + (b-d)\).

Step by step solution

01

Understand Function Subtraction

Firstly, you need to understand what subtracting functions means. If you have two functions, \(f(x)\) and \(g(x)\), their difference, denoted \(f(x)-g(x)\), simply involves subtracting each corresponding element in \(g(x)\) from \(f(x)\). Therefore, \(f(x) - g(x) = f(x) - g(x)\), where \(x\) is the element in the domain over which they are defined.
02

Apply Function Subtraction

Once you understand function subtraction, the next step is to apply it on the given functions. If function \(f\) is represented as \(f(x) = ax + b\) and function \(g\) as \(g(x) = cx + d\), the difference \(f(x) - g(x)\) will be \(f(x) - g(x) = (ax + b) - (cx + d)\).
03

Simplify the Expression

The last step is to simplify the resulting expression from step 2. This involves dealing with the brackets and combining like terms, if any. Using the distributive property of subtraction, the equation from step 2 simplifies to \(f(x) - g(x) = ax + b - cx - d = (a-c)x + (b-d)\). This is the expression for \(f-g\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Begin by graphing the cube root function, \(f(x)-\sqrt[3]{x} .\) Then use transformations of this graph to graph the given function. $$ h(x)-\frac{1}{2} \sqrt[3]{x-2} $$

Begin by graphing the absolute value function, \(f(x)-|x| .\) Then use transformations of this graph to graph the given function. $$ g(x)--2|x+4|+1 $$

What is a piecewise function?

What must be done to a function's equation so that its graph is reflected about the \(x\) -axis?

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The domain of \(f\) is the same as the range of \(f^{-1}\).
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.