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Chapter 2: Problem 71

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

Short Answer

Expert verified
The sum of two functions, \(f\) and \(g\), is obtained by adding the algebraic expressions representing the two functions, \(f(x)\) and \(g(x)\). \((f+g)(x) = f(x) + g(x)\) is the representation of the sum.

Step by step solution

01

Understand Function Operations

In mathematics, two functions can be combined to create a new function through a variety of operations. One such operation is addition. The sum of two functions, \(f\) and \(g\), represented as \(f+g\), is a new function obtained by adding the corresponding values of \(f\) and \(g\).
02

Representation of the Sum Function

The addition of two functions can be represented as follows: if \(f(x)\) is the equation for function \(f\) and \(g(x)\) is the equation for function \(g\), then \(f+g\) is a function whose equation is \(f(x) + g(x)\). This is also commonly represented as \((f+g)(x)\).
03

Find the Sum of the Functions

To find \(f+g\), add the algebraic expressions for \(f(x)\) and \(g(x)\). If there are like terms in the two expressions, combine them. The resulting expression constitutes the equation of function \(f+g\). The operation of function addition is as simple as elementary algebraic addition.
04

Represent the Solution

Write down the mathematical representation of the sum of the functions \(f\) and \(g\), which is \((f+g)(x) = f(x) + g(x)\)

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