Find the domain of the following rational function. $$ f(x)=\frac{4 x}{x-13} $$

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The domain is $$ (-\infty, 13) \cup (13, \infty) $$. To find the domain of the rational function $$ f(x) = \frac{4x}{x-13} $$, we need to identify the values of $$ x $$ for which the function is defined. A rational function is undefined whenever the denominator is equal to zero, because division by zero is undefined. So, we need to find the value of $$ x $$ that makes the denominator $$ x-13 $$ equal to zero: $$ x - 13 = 0 $$ Adding 13 to both sides gives us: $$ x = 13 $$ Therefore, the function is undefined at $$ x = 13 $$. The domain of the function is all real numbers except for $$ x = 13 $$. In interval notation, the domain is: $$ (-\infty, 13) \cup (13, \infty) $$ This means the domain includes all real numbers less than 13 and all real numbers greater than 13, but does not include 13 itself.

Find the domain of the following rational function. \( f(x)=\frac{4 x}{x-13} \)

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Find the domain of the following rational function. \( f(x)=\frac{4 x}{x-13} \)

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