Question

The solution set of $x\ge \frac{1}{x}$ is

• A. $[-1,0]$
• B. $[-1,\infty )$
• C. $[-1,0)\cup [1,\infty )$
• D. $(-\infty ,-1)$

Answer 1

The correct option is C $[-1,0)\cup [1,\infty )$

$x\ge \frac{1}{x}\Rightarrow x-\frac{1}{x}\ge 0\Rightarrow \frac{x^2-1}{x}\ge 0,x\ne 0\Rightarrow \frac{(x+1)(x-1)}{x}\ge 0,x\ne 0$

$\therefore x\in [-1,0)\cup [1,\infty )$