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BITSAT2011MathematicsFunctionsActual

If (f(x)= 1-x 1+x ) the domain of (f⁻¹(x) ) is

Options

  1. A( R )
  2. B( R - -1 )
  3. C((- ,-1) )
  4. D((-1, ) )

Correct answer

B. ( R - -1 )

Step-by-step solution

Let (f(x)=y ). Then ( 1-x 1+x =y ) ( x= 1-y 1+y f⁻¹(y)= 1-y 1+y ) Thus, (f⁻¹(x)= 1-x 1+x ) Clearly, ( f ⁻¹( x ) ) is defined for (1+ x 0 ). Hence, domain of ( f ⁻¹( x ) ) is ( R - -1 )

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