Question

The domain and range of $f(x) = \frac{1}{\sqrt{|x|-x^2}}$ are A and B respectively. Then $A \cup B = $ ?

• A. $\mathbb{R} - \{-1,0,1\}$
• B. $(-1, \infty) - \{0,1\}$
• C. $(-1,0) \cup (0,1) \cup [2, \infty)$
• D. $(-1,1) \cup [2, \infty)$

Hint:

For expressions like $\frac{1}{\sqrt{g(x)}}$, always ensure $g(x)>0$ (not $\geq 0$), because the denominator cannot be zero.

Answer 1

The Correct Option is C