Question

The range of the function $y=\left(\frac{x^2}{1+x^2}\right)$, where $x\in R$ is

• A. $[0,1)$
• B. $[0,1]$
• C. $(0,1)$
• D. $(0,1]$

Answer 1

Answer: (B)

$[0,1]$

$y=\frac{x^2}{1+x^2}\Rightarrow x^{2}y+y=x^2\left(bycrossmultiplication\right)\Rightarrow x^2(y-1)+y=0$

$D\ge 00-4(y-1)\left(y\right)\ge 0\left(takingaquadraticequationonx\right)-4\left(y\right)(y-1)\ge 04\left(y\right)(y-1)\le 0\left(y\right)(y-1)\le 0$

$\therefore yϵ[0,1]$