To determine the domain of the rational function [tex]\( R(x) = \frac{9x}{x + 17} \)[/tex], follow these steps:
1. Identify the denominator: The denominator of the function is [tex]\( x + 17 \)[/tex].
2. Find where the denominator equals zero: A rational function is undefined wherever its denominator is zero, because division by zero is undefined. Solve for [tex]\( x \)[/tex] where the denominator equals zero:
[tex]\[
x + 17 = 0
\][/tex]
[tex]\[
x = -17
\][/tex]
3. Determine the domain: The domain of the function is all real numbers except where the denominator is zero. Therefore, [tex]\( x \)[/tex] cannot be [tex]\(-17\)[/tex].
Based on these steps, the domain of [tex]\( R(x) \)[/tex] is all real numbers except [tex]\( x = -17 \)[/tex].
Hence, the correct choice is:
A. The domain of [tex]\( R(x) \)[/tex] is [tex]\( \{ x \mid x \neq -17 \} \)[/tex].
