Problem 71 - College Algebra

Question

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

Step-by-Step Solution

Answer

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 1: 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 \(g\).

Step 2: 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 \((f+g)(x)\).

Step 3: 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.

Step 4: Represent the Solution

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