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Manipal MET2010MathematicsFunctions

The range of the function f(x)= _e (3 x^2-4 x+5 ) is

Options

  1. A(- , _e 11 3 ]
  2. B[ _e 11 3 , )
  3. C[- _e 11 3 , _e 11 3 ]
  4. DNone of the above

Correct answer

B. [ _e 11 3 , )

Step-by-step solution

aligned & f(x) is defined, if 3 x^2-4 x+5 0 & 3 [x^2- 4 3 x+ 5 3 ] 0 aligned 3 [ (x- 2 3 )^2+ 11 9 ] 0 which is true for all real x . aligned & Domain of f=(- , ) & Let y= _e (3 x^2-4 x+5 ) e^y=3 x^2-4 x+5 & 3 x^2-4 x+ (5-e^y )=0 aligned For x to be real, 16-12 (5-e^y ) 0 12 e^y 44 e^y 11 3 y _e 11 3 Range of f= [ _e 11 3 , )

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