Question

The range of $f\left(x\right)=\frac{x^2-1}{\left|x\right|-1}+x$, is

• A. $R-\left\{3\right\}$
• B. $[0,\infty )-\left\{3\right\}$
• C. $R-\{1,3\}$
• D. $[1,\infty )-\left\{3\right\}$

Answer 1

Answer: (A)

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

Interval	x<-1	-1<x<0	$0\le x<1$	x>1
Function behavior	1	1	2x+1	2x+1

$\therefore {lim}_{x\to 1-}(2x+1)=3$

$1\le f\left(x\right)<3,or,f\left(x\right)>3$

$\therefore f\left(x\right)=R-\left\{3\right\}$