Home
Class 12
MATHS
f(x)=[x]+|1-x|.-1leq x leq 3 where [x] i...

`f(x)=[x]+|1-x|.-1leq x leq 3` where `[x]` is the greatest integer function.Sttaement 1 : `f` is not continuous at `x = 0, 1 , 2 and 3`. Statement 2 : `f(x)=(-x, -1 leq x lt 0 and 1-x,0 leq x lt 1 and 1+x, 1leq xleq 2 and 2+x, 2leq x leq 3`

Promotional Banner

Similar Questions

Explore conceptually related problems

f(x) = 1 + [cosx]x in 0 leq x leq pi/2 (where [.] denotes greatest integer function) then

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

If f(x)={|1-4x^2|,0lt=x<1 and [x^2-2x],1lt=x<2 where [.] denotes the greatest integer function, then

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)={{:(,x[x], 0 le x lt 2),(,(x-1)[x], 2 le x lt 3):} where [.] denotes the greatest integer function, then continutity and diffrentiability of f(x)

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 continutity and diffrentiability of f(x)

Let f(x)=1+x , 0 leq x leq 2 and f(x)=3−x , 2 lt x leq 3 . Find f(f(x)) .

Prove that the greatest integer function defined by f(x) =[x] ,0 lt x lt 2 is not differentiable at x=1

If f(x)= {(|1-4x^2|,; 0 lt= x lt 1), ([x^2-2x],; 1 lt= x lt 2):} , where [.] denotes the greatest integer function, then f(x) is

If sin2x=cos3x and 0 leq x lt pi/2 then x=