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  4. Let f(x)=(x/1-x),x≠ 1 then range of f is

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

Relations and Functions

Solution:

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 $=(-\infty,-1)\cup(-1,\infty)$.