If `f(x)={{:(,x[x], 0 le x lt 2),(,(x-1)[x], 2 le x lt 3):}` where [.] denotes the greatest integer function, then (x) is continuous at x=2

f(x) {(|x-(1)/(2)|",",0 le x lt 1),(x[x]",",1 le x lt 2):} where [.] denotes the greatest integer function. Show that f(x) is continuous at x=1 but not differentiable at x=1.

If f(x)=e^(sin(x-[x])cospix) , where [x] denotes the greatest integer function, then f(x) is

If f(x)=(sin([x]pi))/(x^2+x+1) , where [dot] denotes the greatest integer function, then

If f(x)=cos[pi/x] cos(pi/2(x-1)) ; where [x] is the greatest integer function of x ,then f(x) is continuous at :

f(x)=log(x-[x]) , where [*] denotes the greatest integer function. find the domain of f(x).

The function f(x) = [x] cos((2x-1)/2) pi where [ ] denotes the greatest integer function, is

domin of f(x)=sin^-1[log_2(x^2/2)] where [ . ] denotes the greatest integer function.

If f(x) = [x] , where [*] denotes greatest integral function. Then, check the continuity on (1, 2]

f(x)=sin^(-1)[2x^(2)-3] , where [*] denotes the greatest integer function. Find the domain of f(x).

Prove that f(x) = [tan x] + sqrt(tan x - [tan x]) . (where [.] denotes greatest integer function) is continuous in [0, (pi)/(2)) .