Q156 / 270 · NDA 2016 (Phase 1) · Mathematics

What is the range of the function $\mathrm{y}=\frac{\mathrm{x}^2}{1+\mathrm{x}^2}$, where $\mathrm{x} \in \mathrm{R}$ ?

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

Solution

Function $y=\frac{x^2}{1+x^2} \quad x \in R$ $x=0$ $y=0$ $\begin{array}{ll} x=1,-1 & y=\frac{1}{2} \\ x=2,-2 & y=\frac{4}{5} \\ x=3,-3 & y=\frac{9}{10} \end{array}$ . . . . Clearly $0 \leq y \lt 1$ $\Rightarrow y \in[0,1)$ Hence Range of $y=[0,1)$

Hence, the correct answer is option: 'A'.

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