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The given mathematical function is:

\[
f(x) = \frac{1}{x - 3}
\]

The function \( f(x) \) is undefined when the denominator is equal to zero, as division by zero is undefined in mathematics. To find the value of \( x \) where the function is not defined, set the denominator equal to zero and solve for \( x \):

\[
x - 3 = 0
\]
\[
x = 3
\]

Therefore, the function \( f(x) \) is defined for all real numbers \( x \), except \( x = 3 \). 

In conclusion, the function is undefined for \( x = 3 \), and it is defined for all other real numbers.

Would you like any further details or explanations?

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Here are 5 related questions for further exploration:
1. What happens to the value of \( f(x) \) as \( x \) approaches 3?
2. How do you find the domain of other rational functions?
3. What is the range of the function \( f(x) = \frac{1}{x - 3} \)?
4. Can you graph the function \( f(x) = \frac{1}{x - 3} \) and identify any asymptotes?
5. How do you solve equations involving functions like \( f(x) = \frac{1}{x - 3} \)?

**Tip**: To find where a function is undefined, always look for values that make the denominator zero or result in taking an even root of a negative number.

Fungsi f(x) = 1 / (x - 3) terdefinisi untuk semua bilangan riil x, kecuali...

Learn how to find the domain of the rational function f(x) = 1 / (x - 3) by determining where the denominator is zero. This example explores key concepts in functions and rational expressions. Suitable for Grades 10-12.

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