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Manipal MET2020MathematicsFunctions

If f(x)= _e (6- |x^2+x-6 | ) , then domain of f(x) has how many integral values of x ?

Options

  1. A5
  2. B4
  3. CInfinite
  4. DNone of these

Correct answer

D. None of these

Step-by-step solution

Given, f(x)= _e (6- |x^2+x-6 | ) The function f(x) is defined, if array lr & (6- |x^2+x-6 | ) 0 & |x^2+x-6 | 6 & -6 x^2+x-6 6 If & x^2+x-6 6 & x^2+x-12 0 & (x+4)(x-3) 0 array x (-4,3) ....(i) Now, if -6 x^2+x-6 x^2+x 0 x(x+1) 0 From Eqs. (i) and (ii), we get x (0,3) f(x) has only two integral values. x=1,2

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