Question

Which of the following is/are true?

• A. $\frac{1}{x}\ge 2\Rightarrow x\ge \frac{1}{2}$
• B. $\frac{1}{x}>2\Rightarrow x<\frac{1}{2}$
• C. $\frac{1}{x}>2\Rightarrow 0<x<\frac{1}{2}$
• D. $\frac{1}{x}\ge 2\Rightarrow 0<x\le \frac{1}{2}$

Answer 1

Answer: (C), (D)

The correct options are
C $\frac{1}{x}>2\Rightarrow 0<x<\frac{1}{2}$
D $\frac{1}{x}\ge 2\Rightarrow 0<x\le \frac{1}{2}$

$\frac{1}{x}>2\Rightarrow \frac{1}{x}\in (2,\infty )\Rightarrow x\in (0,\frac{1}{2})$
$\frac{1}{x}\ge 2\Rightarrow \frac{1}{x}\in [2,\infty )\Rightarrow x\in (0,\frac{1}{2}]$