JEE Main2012MathematicsContinuity and DifferentiabilityActual
If f : R R is a function defined by f(x)=[ x ] ( 2 x-1 2 ) , where [ x ] denotes the greatest integer function, then f is
Options
- Acontinuous for every real x
- Bdiscontinuous only at x=0
- Cdiscontinuous only at non-zero integral values of x
- Dcontinuous only at x=0
Correct answer
A. continuous for every real x
Step-by-step solution
f(x)=[x] ( 2 x-1 2 ) =[x] (x- 1 2 ) =[x] x is continuous for every real x .