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
Create a free account to view solution
View Solution FreeMore Function Questions
Let f : R → R be a function defined by f(x) = x + √x2, then f is-...If f : (e, ∞) → R & f(x) f(x) = log [log(log x)], then is -...Which of the following functions are homogeneous ?...If f : R → R, f(x) = x3 + 3, and g : R → R, g(x) = 2x + 1, then f−1log−1(23) equals-...If domain of f(x) is (- ∞ , 0], then domain of f(6{x}2 - 5 {x} + 1) is (where {.} represents fractional part funct...