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BITSAT2009MathematicsTrigonometric Ratios & IdentitiesActual

If the function (f:(- , ) B ) defined by (f(x)=-x^2+6 x-8 ) is bijective, then (B= )

Options

  1. A([1, ) )
  2. B((- , 1] )
  3. C((- , ) )
  4. DNone of these

Correct answer

B. ((- , 1] )

Step-by-step solution

Since the function (f ) is bijective, therefore (f ) is onto. Therefore range of (f=B ). Let (y=-x^2+6 x-8 ) ( x ^2-6 x +(8+ y )=0 ) ( x= 6 36-4(8+y) 2 = 6 4-4 y 2 ) For (x ) to be real, (4-4 y 0 y 1 ) ( B = ) range of ( F =(- , 1] )

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