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NDA 2010
Exam
NDA
Year
2010
Subject
Mathematics
Chapter
Functions

NDA 2010 · Mathematics · Functions

The function f(x)=(x)/(x^2+1) from R to R is

The function f(x)=xx2+1f(x)=\frac{x}{x^2+1} from R to R is

Options

  1. AOne-one as well as onto
  2. BOnto but not one-one
  3. CNeither one-one nor onto
  4. DOne-one but not onto

Correct answer

C. Neither one-one nor onto

Step-by-step solution

f(x)=xx2+1f(x1)=x1x12+1,f(x2)=x2x22+1f(x1)=f(x2)\begin{aligned} & f(x)=\frac{x}{x^2+1} \\ & f\left(x_1\right)=\frac{x_1}{x_1^2+1}, \quad f\left(x_2\right)=\frac{x_2}{x_2^2+1} \\ & f\left(x_1\right)=f\left(x_2\right)\end{aligned}x1x12+1=x2x22+1 or  x1x22+x1=x2x12+x2 or x1x22−x2x12=x2−x1x1x2=1\begin{aligned} & \frac{x_1}{x_1^2+1}=\frac{x_2}{x_2^2+1} \\ & \text{\text{ or } } x_1 x_2^2+x_1=x_2 x_1^2+x_2 \\ & \text{ or } x_1 x_2^2-x_2 x_1^2=x_2-x_1 \\ & x_1 x_2=1 \end{aligned}f$ is neither one-one nor onto.
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