Chapter 9.9, Problem 44PPS

To determine

To describe sometime, always or never true.

Answer to Problem 44PPS

Always

Explanation of Solution

Given information:

  $f(x)$ and $g(x)$are linear functions

  $(f+g)(x)$is all real numbers.

Suppose we have two functions, $f(x)$ and $g(x)$ . We can define the sum of these two functions by,

  $(f+g)(x)=f(x)+g(x),$

where x is in the domain of both f and g .

For example, we can add the functions $f(x)=x-1$and $g(x)=2x+3$ as,

  $(f+g)(x)=f(x)+g(x)$

  $=x-1+2x+3$ = 3x + 2 .

The domain of $(f+g)(x)$ consists of all x -values that are in the domain of both f and g . In this example, f and g both have domain consisting of all real numbers, therefore, $(f+g)(x)$ also has domain consisting of all real numbers.

If $f(x)$ and $g(x)$are linear functions then $(f+g)(x)$is always a all real numbers.