If the function f:\mathbf{R}-\left \{ 1,-1 \right \}\rightarrow A\; defined by f\left ( x \right )=\frac{x^{2}}{1-x^{2}} \; , is surjective , then A is equal to :

  • Option 1)

     \textbf{R}-\left \{ -1 \right \}            

  • Option 2)

     \left [ 0,\infty )

  • Option 3)

     \textbf{R}-\left [ -1,0 )

  • Option 4)

    \textbf{R}-\left ( -1,0 \right )

 

Answers (2)

Let y=\frac{x^{2}}{1-x^{2}}\Rightarrow y-yx^{2}=x^{2}

     x^{2}=\frac{y}{y+1}

\therefore \; \; x^{2}\geqslant 0\Rightarrow \frac{y}{y+1}\geqslant 0

\Rightarrow y\epsilon \left ( -\infty ,1 \right )\upsilon \left [ 0,\infty )

   OR 

\textbf{R}-\left [ -1,0 )


Option 1)

 \textbf{R}-\left \{ -1 \right \}            

Option 2)

 \left [ 0,\infty )

Option 3)

 \textbf{R}-\left [ -1,0 )

Option 4)

\textbf{R}-\left ( -1,0 \right )

SIMPLY TO SAVE YOUR TIME DO OPTION VERIFICATION

 

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