Question

Value of $x$ satisfying $\left|\frac{x}{\left|x\right|}\right|=\frac{x}{\left|x\right|}$ is/are

• A. $x\in R$
• B. $x\in R-\left\{0\right\}$
• C. $x\in R^{+}$
• D. $x\in R^{-}$

Answer 1

The correct option is C $x\in R^{+}$

Any real number divided by its absolute value will either be $1$ or $-1,$

So $\frac{x}{\left|x\right|}=1,$ when $x>0$ and $-1,$ when $x<0$

But $\left|\frac{x}{\left|x\right|}\right|$ will always be equal to $1$.

So, $\left|\frac{x}{\left|x\right|}\right|=\frac{x}{\left|x\right|}$ only when $x>0\Rightarrow x\in R^{+}$