JEE Main 2014 · 19 Apr · Shift 1 · Mathematics Q61

MathematicsSingle correct+4 / -1Question 61 of 90

Let $f:\mathbb R\to\mathbb R$ be defined by $f(x)=\dfrac{|x|-1}{|x|+1}$ then $f$ is :

both one - one and onto

one - one but not onto

onto but not one - one

neither one - one nor onto.

Answer and worked solution

Official answer: D

$f(-x)=f(x)$ , so $f$ is not one-one ( $f(1)=f(-1)=0$ ). For all $x$ , $-1\le f(x)<1$ , so values such as 2 are never reached and $f$ is not onto.

JEE Main 2014 · 19 Apr · Shift 1, Mathematics question 61