To determine the domain of the function [tex]\( f(x) = \frac{x-3}{7x} \)[/tex], we need to identify the values of [tex]\( x \)[/tex] for which the function is undefined.
A function is undefined whenever the denominator is zero because division by zero is not allowed. In this case, the denominator of the function is [tex]\( 7x \)[/tex].
Let's solve for [tex]\( x \)[/tex] when the denominator equals zero:
[tex]\[ 7x = 0 \][/tex]
Solving for [tex]\( x \)[/tex]:
[tex]\[ x = 0 \][/tex]
So, the function [tex]\( f(x) = \frac{x-3}{7x} \)[/tex] is undefined when [tex]\( x = 0 \)[/tex].
Therefore, the domain of the function is all real numbers except [tex]\( 0 \)[/tex].
The correct answer is:
All real numbers except 0
