College Math Placement Practice Test

What is the domain of the function f(x) = 1/(x - 2)?

1. All real numbers

2. x ≠ 0

3. x ≠ 1

4. x ≠ 2

The correct answer is: x ≠ 2

The domain of a function consists of all the values that the independent variable, in this case \( x \), can take without causing the function to be undefined. For the function \( f(x) = \frac{1}{x - 2} \), the denominator \( (x - 2) \) cannot equal zero since division by zero is undefined. To find where this occurs, set the denominator equal to zero: \[ x - 2 = 0 \] Solving this gives: \[ x = 2 \] Thus, the function \( f(x) \) is undefined when \( x = 2 \). Therefore, all real numbers are included in the domain except for \( x = 2 \). This leads to the conclusion that the domain of the function is all real numbers except for 2, which is expressed as \( x \neq 2 \). The other choices, while referring to other values or conditions, do not reflect the true restriction on the function's domain as accurately as the correct choice does. The correct answer clearly defines the specific value that causes the function to be undefined.