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AP EAMCET201922 Apr 2019Morning ShiftMathematicsFunctionsActual

If (f: A B ) is an onto function such that (f(x)= |x|-x + 1 |x|-x ), then (A ) and (B ) are respectively.

Options

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

Correct answer

B. ((- , 0),[2, ) )

Step-by-step solution

We have, (f(x)= |x|-x + 1 |x|-x ) We know that, (f(x) ) will be defined when ( array lrl & & |x|-x > 0 & & |x| > x & x (- , 0) array ) Now, ( aligned & f(x)= |x|-x + 1 |x|-x & = -2 x + 1 -2 x [ x (- , 0)] & f_ =2 -2 x 1 -2 x [ A M G M] & =2 & A=(- , 0) and B=[2, ) aligned ) ( f(x) [2, ) )

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