What Is { (f-g)(x)$} ? G I V E N : ?Given: ? G I V E N : { F(x) = 3x^5 + 6x^2 - 5 \} ${ G(x) = 2x^4 + 7x^2 - X + 16 } E N T E R Y O U R A N S W E R I N S T A N D A R D F O R M I N T H E B O X . Enter Your Answer In Standard Form In The Box. E N T Eryo U R An S W Er In S T An D A R Df Or Min T H E B O X . { (f-g)(x) =\$}

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Introduction to Function Subtraction

In mathematics, functions are a fundamental concept that plays a crucial role in various branches of mathematics, including algebra, calculus, and analysis. When dealing with functions, it is often necessary to perform operations on them, such as addition, subtraction, multiplication, and division. In this article, we will focus on the concept of function subtraction, specifically the expression {(f-g)(x)$}$, where {f(x)$] and [$g(x)$] are given functions.

Understanding Function Notation

Before we dive into the concept of function subtraction, let's briefly review function notation. A function [f(x)$]isarelationbetweenasetofinputs,calledthedomain,andasetofpossibleoutputs,calledtherange.Thefunctionistypicallydenotedas\[f(x)\$] is a relation between a set of inputs, called the domain, and a set of possible outputs, called the range. The function is typically denoted as \[f: \mathbb{R} \to \mathbb{R}$], where [R$]representsthesetofallrealnumbers.Theinputvalue,\[\mathbb{R}\$] represents the set of all real numbers. The input value, \[x$, is also known as the independent variable, while the output value, [$f(x)$, is also known as the dependent variable.

Function Subtraction: [$(f-g)(x)$]

Now that we have a basic understanding of function notation, let's move on to the concept of function subtraction. The expression [(f−g)(x)$]representsthedifferencebetweentwofunctions,\[(f-g)(x)\$] represents the difference between two functions, \[f(x)$] and [g(x)$.Toevaluatethisexpression,weneedtosubtractthevalueof\[g(x)\$. To evaluate this expression, we need to subtract the value of \[g(x)$] from the value of [$f(x)$. This can be done by subtracting the corresponding terms of the two functions.

Evaluating [$(f-g)(x)$] for Given Functions

Let's consider the given functions:

[ f(x) = 3x^5 + 6x^2 - 5 } { g(x) = 2x^4 + 7x^2 - x + 16 }$

To evaluate {(f-g)(x)$, we need to subtract the corresponding terms of the two functions:

[ (f-g)(x) = (3x^5 + 6x^2 - 5) - (2x^4 + 7x^2 - x + 16) }$

Simplifying the Expression

Now, let's simplify the expression by combining like terms:

(f−g)(x)=3x5−2x4+(6x2−7x2)+(−5−(−x)+16){ (f-g)(x) = 3x^5 - 2x^4 + (6x^2 - 7x^2) + (-5 - (-x) + 16) }

(f−g)(x)=3x5−2x4−x2+11{ (f-g)(x) = 3x^5 - 2x^4 - x^2 + 11 }

Conclusion

In conclusion, the expression [(f−g)(x)$]representsthedifferencebetweentwofunctions,\[(f-g)(x)\$] represents the difference between two functions, \[f(x)$] and [g(x)$.Toevaluatethisexpression,weneedtosubtractthecorrespondingtermsofthetwofunctionsandsimplifytheresultingexpression.Inthisarticle,wehaveevaluatedtheexpression\[g(x)\$. To evaluate this expression, we need to subtract the corresponding terms of the two functions and simplify the resulting expression. In this article, we have evaluated the expression \[(f-g)(x)$] for the given functions [f(x)=3x5+6x2−5$]and\[f(x) = 3x^5 + 6x^2 - 5 \$] and \[g(x) = 2x^4 + 7x^2 - x + 16 $]. The resulting expression is [$(f-g)(x) = 3x^5 - 2x^4 - x^2 + 11 $].

Final Answer

The final answer is: 3x5−2x4−x2+113x^5 - 2x^4 - x^2 + 11

Discussion

The concept of function subtraction is a fundamental idea in mathematics that has numerous applications in various branches of mathematics, including algebra, calculus, and analysis. In this article, we have evaluated the expression [(f−g)(x)$]forthegivenfunctions\[(f-g)(x)\$] for the given functions \[f(x) = 3x^5 + 6x^2 - 5 $] and [g(x)=2x4+7x2−x+16$].Theresultingexpressionis\[g(x) = 2x^4 + 7x^2 - x + 16 \$]. The resulting expression is \[(f-g)(x) = 3x^5 - 2x^4 - x^2 + 11 $]. We hope that this article has provided a clear understanding of the concept of function subtraction and its applications in mathematics.

Introduction

In our previous article, we discussed the concept of function subtraction, specifically the expression [(f−g)(x)$,where\[(f-g)(x)\$, where \[f(x)$] and [$g(x)$] are given functions. In this article, we will address some common questions and concerns related to function subtraction.

Q1: What is the difference between function addition and function subtraction?

A1: Function addition and function subtraction are two fundamental operations in mathematics that involve combining or subtracting functions. Function addition involves combining two or more functions by adding their corresponding terms, while function subtraction involves subtracting one function from another.

Q2: How do I evaluate the expression [(f−g)(x)$]whenthefunctions\[(f-g)(x)\$] when the functions \[f(x)$] and [$g(x)$] are not given?

A2: To evaluate the expression [(f−g)(x)$,youneedtohavetheexplicitexpressionsforthefunctions\[(f-g)(x)\$, you need to have the explicit expressions for the functions \[f(x)$] and [g(x)$.Ifthefunctionsarenotgiven,youcannotevaluatetheexpression\[g(x)\$. If the functions are not given, you cannot evaluate the expression \[(f-g)(x)$.

Q3: Can I simplify the expression [$(f-g)(x)$] by combining like terms?

A3: Yes, you can simplify the expression [$(f-g)(x)$] by combining like terms. This involves combining the terms with the same variable and exponent.

Q4: What is the difference between [(f−g)(x)$]and\[(f-g)(x)\$] and \[(g-f)(x)$]?

A4: The expressions [(f−g)(x)$]and\[(f-g)(x)\$] and \[(g-f)(x)$] are not equal. The expression [(f−g)(x)$]representsthedifferencebetweenthefunctions\[(f-g)(x)\$] represents the difference between the functions \[f(x)$] and [g(x)$,whiletheexpression\[g(x)\$, while the expression \[(g-f)(x)$] represents the difference between the functions [g(x)$]and\[g(x)\$] and \[f(x)$].

Q5: Can I use the distributive property to simplify the expression [$(f-g)(x)$]?

A5: Yes, you can use the distributive property to simplify the expression [(f−g)(x)$.Thisinvolvesdistributingthenegativesigntoeachterminthefunction\[(f-g)(x)\$. This involves distributing the negative sign to each term in the function \[g(x)$.

Q6: What is the significance of function subtraction in real-world applications?

A6: Function subtraction has numerous applications in real-world problems, such as physics, engineering, and economics. For example, in physics, function subtraction can be used to model the motion of objects, while in engineering, it can be used to design and optimize systems.

Q7: Can I use function subtraction to solve systems of equations?

A7: Yes, you can use function subtraction to solve systems of equations. This involves subtracting one equation from another to eliminate variables and solve for the remaining variables.

Q8: What are some common mistakes to avoid when evaluating the expression [$(f-g)(x)$]?

A8: Some common mistakes to avoid when evaluating the expression [$(f-g)(x)$] include:

  • Not combining like terms
  • Not distributing the negative sign to each term in the function [$g(x)$
  • Not simplifying the expression by combining like terms
  • Not using the correct order of operations

Conclusion

In conclusion, function subtraction is a fundamental concept in mathematics that has numerous applications in various branches of mathematics, including algebra, calculus, and analysis. In this article, we have addressed some common questions and concerns related to function subtraction, including the difference between function addition and function subtraction, how to evaluate the expression [(f−g)(x)$,andcommonmistakestoavoidwhenevaluatingtheexpression\[(f-g)(x)\$, and common mistakes to avoid when evaluating the expression \[(f-g)(x)$. We hope that this article has provided a clear understanding of the concept of function subtraction and its applications in mathematics.

Final Answer

The final answer is: 3x5−2x4−x2+113x^5 - 2x^4 - x^2 + 11

Discussion

The concept of function subtraction is a fundamental idea in mathematics that has numerous applications in various branches of mathematics, including algebra, calculus, and analysis. In this article, we have addressed some common questions and concerns related to function subtraction, including the difference between function addition and function subtraction, how to evaluate the expression [(f−g)(x)$,andcommonmistakestoavoidwhenevaluatingtheexpression\[(f-g)(x)\$, and common mistakes to avoid when evaluating the expression \[(f-g)(x)$. We hope that this article has provided a clear understanding of the concept of function subtraction and its applications in mathematics.