Question

unit: functions
problems
find the domain of ( f(x) = \frac{7x}{x - 3} ).
options:

• all real numbers except 3
• all real numbers except 7
• all real numbers except 0
• all real numbers except -3

Explanation:

Step1: Identify the function type

The function \( f(x)=\frac{7x}{x - 3} \) is a rational function. For rational functions, the denominator cannot be zero (since division by zero is undefined).

Step2: Set the denominator not equal to zero

We set the denominator \( x - 3
eq0 \).

Step3: Solve for x

Solving the inequality \( x - 3
eq0 \), we add 3 to both sides to get \( x
eq3 \). So the domain of the function is all real numbers except \( x = 3 \).

Answer:

A. All real numbers except 3