FunctionHard
Question
If f : R → R is a function defined by f(x) = [x] cos 
, where [x] denotes the greatest integer function, then f is :
, where [x] denotes the greatest integer function, then f is :Options
A.continuous only at x = 0.
B.continuous for every real x.
C.discontinuous only at x = 0.
D.discontinuous only at non-zero integralvalues of x.
Solution
[x] is contincous at R - I
∴ f(x) is continuous at R - I
Now At x = I
LHL =
similarly,
RHL = 0 and f(I) = 0
∴ Function is continous everywhere
∴ f(x) is continuous at R - I
Now At x = I
LHL =
similarly,
RHL = 0 and f(I) = 0
∴ Function is continous everywhere
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