Question

unit: functions
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find the domain of $f(x) = \frac{6x}{x + 3}$.
\bigcirc all real numbers except 3
\bigcirc all real numbers except 0
\bigcirc all real numbers except 6
\bigcirc all real numbers except $-3$

Explanation:

Step1: Recall domain of rational function

For a rational function \( f(x)=\frac{g(x)}{h(x)} \), the domain excludes values where \( h(x) = 0 \) (since division by zero is undefined). Here, \( h(x)=x + 3 \).

Step2: Solve \( h(x)=0 \)

Set \( x + 3=0 \). Solving for \( x \), we get \( x=-3 \). So the domain is all real numbers except \( x = - 3 \).

Answer:

All real numbers except \( -3 \) (the option corresponding to this, e.g., if the last option is "All real numbers except \( -3 \)", then the answer is that option. Assuming the last option is D. All real numbers except \( -3 \), the answer is D. All real numbers except \( -3 \))