Identify the conditions for the function to be defined in real numbers.

April 13, 2026Computer Science

ScanSolve AI Answer

2 stepsApril 13, 2026

Answer

\sqrt{\frac{2}{x-2}} - 3$.

Step 1: Identify the conditions for the function to be defined in real numbers. The given function is $f(x) = \sqrt{\frac{2}{x-2}} - 3$ . For $f(x)$ to be a real number, two conditions must be met:

The expression under the square root must be non-negative: $\frac{2}{x-2} \ge 0$ .
The denominator of the fraction cannot be zero: $x-2 \ne 0$ .

Step 2: Apply the condition for the denominator. From $x-2 \ne 0$ , we know that $x \ne 2$ .

Step 3: Apply the condition for the square root. For $\

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Quick Answer

The given function is f(x) = sqrt((2)/(x-2)) - 3.
For f(x) to be a real number, two conditions must be met: 1.
The expression under the square root must be non-negative: (2)/(x-2) 0.
The denominator of the fraction cannot be zero: x-2 0.

Asked on April 13, 2026Computer Science

This computer science problem involves algorithmic thinking and programming concepts. The solution below explains the approach, logic, and implementation step by step.

ScanSolve AI AnswerAnswered on April 13, 2026

Step 1: Identify the conditions for the function to be defined in real numbers. The given function is f(x) = sqrt((2)/(x-2)) - 3. For f(x) to be a real number, two conditions must be met: 1. The expression under the square root must be non-negative: (2)/(x-2) 0. 2. The denominator of the fraction cannot be zero: x-2 0. Step 2: Apply the condition for the denominator. From x-2 0, we know that x 2. Step 3: Apply the condition for the square root. For $\