Question

The range of $y=\frac{x-1}{2x-7},x\ne \frac{7}{2}$ is

• A. $R$
• B. $R-\left\{1\right\}$
• C. $R-\left\{\frac{1}{2}\right\}$
• D. $R-\left\{0\right\}$

Answer 1

The correct option is C $R-\left\{\frac{1}{2}\right\}$

$y=\frac{x-1}{2x-7}$
$\Rightarrow 2xy-7y=x-1$
$\Rightarrow x(2y-1)=7y-1$
$\Rightarrow x=\frac{7y-1}{2y-1}$
$\therefore y\in R-\left\{\frac{1}{2}\right\}$