`f(x)=|x-r|; r-1 le x le r + 1 and =1 ; r + 1 < x < r + r` Find the fundamental period of `f(x),` if at all `f(x)` is periodic.

Let f be a function on R given by f(x) = x^(2) and let E = {x in R: - 1 le x le 0 } and F = { x in R , 0 le x le 1 } then which of the following is fase ?

If f(x)=x(x-1), 0 le x le 1, and f(x+1)=f(x) AA x in R , then |int_(2)^(4)f(x)dx| is _____________

(x+3)/(x-1)le1/2,x ne1 and x in R

Let the straight line x=b divide the area enclosed by y=(1-x)^2, y=0 and x=0 into two parts R_1 (0 le x le b) and R_2 (b le x le 1) such that R_1-R_2=1/4 . Then b equals (A) 3/4 (B) 1/2 (C) 1/3 (D) 1/4

Let the straight line x=b divide the area enclosed by y=(1-x)^2, y=0 and x=0 into two parts R_1 (0 le x le b) and R_2(b le x le 1) such that R_1-R_2=1/4 .Then b equals :

Let the straight line x =b divide the area enclosed by y=(1-x)^(2) y=0 and x=0 in to parts R_(1)(0 le x le b) and R_(2) (b le x le 1) such that R_(1)-R_(2)=1/4 then b equals

Let the straight line x = b divide the area enclosed by y = (1-x)^(2), y = 0 and x = 0 into two parts R_(1) (0 le x le b) and R_(2) (b le x le 1) such that R_(1) - R_(2) = 1/4 . Then b equals

Suppose f:[-2,2] to R is defined by f(x)={{:(-1 " for " -2 le x le 0),(x-1 " for " 0 le x le 2):} , then {x in [-2,2]: x le 0 and f(|x|)=x}=