Question

The range of the function $y=\frac{x^2}{1+x^2}$

• A. $[0,1)$
• B. $[0,2)$
• C. $[0,\infty )$
• D. none of these

Answer 1

The correct option is A $[0,1)$

clearly $y=\frac{x^2}{1+x^2}\ge 0$ for all $x\in R$
now, $y=\frac{1}{1+\frac{1}{x^2}}$
As $x\to \infty$, $y\to 1$
Therefore, $R\in [0,1)$