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AP EAMCET2008MathematicsFunctions

If f: R R and g: R R are defined by f(x)=|x| and g(x)=[x-3] for x R , then g(f(x)):- 8 5 < x < 8 5 is equal to

Options

  1. A0,1
  2. B1,2
  3. C-3,-2
  4. D2,3

Correct answer

C. -3,-2

Step-by-step solution

Given that, f(x)=|x| and g(x)=[x-3] For - 8 5 < x < 8 5 , 0 f(x) < 8 5 Now, for 0 f(x) < 1 , aligned g(f(x)) & =[f(x)-3] & =-3[ -3 f(x)-3 < -2] aligned Again, for 1 f(x) < 1.6 g(f(x))=-2 Hence, required set is -3,-2 .

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