# Chapter 7 - Functions and Graphs - 7.4 The Algebra of Functions - 7.4 Exercise Set: 63

$\color{blue}{(-\infty, -4.5) \cup (-4.5, 1) \cup (1, +\infty)}$

#### Work Step by Step

RECALL: The domain of the sum, difference, and product of $f(x)$ and $g(x)$ is the common elements of the domains of the two functions. The domain of the respective functions are: For $f(x)$, $-4.5$ will make the denominator zero so its domain is: $(-\infty, -4.5) \cup (-4.5, +\infty)$ $g(x)$ is defined for all real numbers except $1$ (as it makes the denominator zero) so its domain is: $(-\infty,1) \cup (1, +\infty)$. Note that: $[(-\infty, -4.5) \cup(-4.5, +\infty)] \cap [(-\infty, 1) \cup (1, +\infty)] \\= (-\infty, -4.5) \cup (-4.5, 1) \cup (1, +\infty)$. Thus, the domain of the sum, difference, and product of $f(x)$ and $g(x)$ is: $\color{blue}{(-\infty, -4.5) \cup (-4.5, 1) \cup (1, +\infty)}$

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