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AP EAMCET2006MathematicsFunctions

If f: R R is defined by f(x)=[2 x]-2[x] for x R , where [x] is the greatest integer not exceeding x , then the range of f is :

Options

  1. Ax R: 0 x 1
  2. B0,1
  3. Cx R: x>0
  4. Dx R: x 0

Correct answer

B. 0,1

Step-by-step solution

f(x)=[2 x]-2[x] x R Let x is an integer, then f(x)=0 and let x is not an integer, then quad f(x)=1 Range of f(x)= 0,1

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