Question

The range of $f\left(x\right)=\frac{2x}{2+3x}$ is

• A. $R$
• B. $R-\left\{\frac{2}{3}\right\}$
• C. $R-\left\{\frac{-2}{3}\right\}$
• D. $R^{+}$

Answer 1

The correct option is B

$R-\left\{\frac{2}{3}\right\}$

$f\left(x\right)=y=\frac{2x}{2+3x}\Rightarrow 2y+3yx=2x\Rightarrow 2y=x(2-3y)\Rightarrow x=\frac{2y}{2-3y}$
$x$ is not defined when $y=\frac{2}{3}$
Hence, the range of f(x) is $R-\left\{\frac{2}{3}\right\}$