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

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

• A. x ∈ ℝ, x ≠ 2
• B. x ∈ ℝ, x ≠ 1
• C. x ∈ ℝ, x ≠ 3
• D. x ∈ ℝ, x ≥ 0

Answer: (A)

To determine the domain of the function f(x) = 1/(x - 2), we need to identify the values of x for which the function is defined. This function is a rational function, and rational functions are undefined when the denominator equals zero. In this case, the denominator is (x - 2). Therefore, we set that equal to zero to find the value that would make the function undefined: x - 2 = 0 x = 2 This means that the function is undefined when x equals 2. Thus, the domain of the function includes all real numbers except for x = 2. In mathematical notation, this is expressed as x ∈ ℝ, x ≠ 2, indicating that the function can take any real number as input except for 2. This is why the correct answer addresses this aspect of the function's behavior, highlighting that all real numbers are permissible values except for the specific point where the denominator leads to an undefined expression.

To determine the domain of the function f(x) = 1/(x - 2), we need to identify the values of x for which the function is defined. This function is a rational function, and rational functions are undefined when the denominator equals zero.

In this case, the denominator is (x - 2). Therefore, we set that equal to zero to find the value that would make the function undefined:

x - 2 = 0

x = 2

This means that the function is undefined when x equals 2. Thus, the domain of the function includes all real numbers except for x = 2.

In mathematical notation, this is expressed as x ∈ ℝ, x ≠ 2, indicating that the function can take any real number as input except for 2. This is why the correct answer addresses this aspect of the function's behavior, highlighting that all real numbers are permissible values except for the specific point where the denominator leads to an undefined expression.