Question

Range of the function $2y+3|x|=x$ is:

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

Answer 1

The correct option is C $R^{-}\cup \left\{0\right\}$

$2y=x-3|x|$
$\Rightarrow y=\{\begin{array}{cc}-x& x\ge 0\\ 2x& x<0\end{array}$
Clearly, $y\le 0$ for $x\in R$
$\therefore$ Range $=(-\infty ,0]=R^{-}\cup \left\{0\right\}$