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AP EAMCET202017 Sep 2020Evening ShiftMathematicsFunctionsActual

The function (f: R R ) defined by (f(x)= x 1+x^2 ) is ........

Options

  1. ASurjective but not injective
  2. BBijective
  3. CInjective but not surjective
  4. DNeither injective nor surjective

Correct answer

C. Injective but not surjective

Step-by-step solution

( aligned & f(x)= x 1+x^2 & f (x₁ )=f(x)₂ x₁ 1+x₁^2 = x₂ 1+x₂^2 aligned ) ( array rlrl & & x₁^2 (1+x₂^2 ) & =x₂^2 (1+x₁^2 ) & & x₁^2 & =x₂^2 x₁ & =x₂ array ) ( F ) is injective in nature Also, Let (f(x)=y= x 1+x^2 ) ( aligned & y^2 (1+x^2 )=x^2 & y^2 1-y^2 =x^2 x= y 1-y^2 aligned ) As (y^2 1 -1 |y| 1 ) So, (f ) is non surjective.

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