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NDA 2016
Exam
NDA
Year
2016
Subject
Mathematics
Chapter
Functions

NDA 2016 · Mathematics · Functions

What is the range of the function y= x^2 1+x^2 , where x ∈ R ?

What is the range of the function y=x21+x2\mathrm{y}=\frac{\mathrm{x}^2}{1+\mathrm{x}^2}, where x∈R\mathrm{x} \in \mathrm{R} ?

Options

  1. A[0,1)[0,1)
  2. B[0,1][0,1]
  3. C(0,1)(0,1)
  4. D(0,1](0,1]

Correct answer

A. [0,1)[0,1)

Step-by-step solution

Function y=x21+x2x∈Rx=0y=0y=\frac{x^2}{1+x^2} \quad x \in Rx=0y=0x=1,−1y=12x=2,−2y=45x=3,−3y=910\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}....Clearly0≤y<1⇒y∈[0,1). . . . Clearly 0 \leq y < 1\Rightarrow y \in[0,1) Hence Range of y=[0,1)y=[0,1)
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