Question

Domain of f(x) = \(\frac{x}{|-|x|}\) is

• A. R - [-1, 1]
• B. (-∞, 1)
• C. (-∞, 1) ∪ (0, 1)
• D. R - {-1, 1}

Answer 1

The Correct Option is D

The function \( f(x) = \frac{x}{|x|} \) involves division by the absolute value of \( x \).
The domain of this function excludes \( x = 0 \), as division by zero is undefined.
Therefore, the domain is all real numbers except \( x = 0 \), or \(\mathbb{R} \setminus \{0\}\).
The function \( f(x) \) is defined for all values except \( x = 1 \) and \( x = -1 \), where it will result in an indeterminate form.

The correct answer is (D) : R - {-1, 1}