Question

Let $f(x)=\frac{x}{1-x},x\ne 1$ then range of $f$ is

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

Answer 1

Answer: (D)

Let $y=f(x)=\frac{x}{1-x}\Rightarrow y-xy=x\Rightarrow y=x(1+y)$
$\therefore x=\frac{y}{1+y}$ which is defined for all y $\in$ R except $y=-1$
$\therefore$ Range $=(-\infty ,-1)\cup (-1,\infty )$.