Let `f(x)=x(2-x), 0<=x<=2`. If the definition of `f` is extended over the set `R-[0,2]`by `f(x+2)=f(x)` then `f(x)` is

Let f(x)=2x(2-x), 0 le x le 2 . Then find the number of solutions of f(f(f(x)))= (x)/(2) .

Let f(x)=2x(2-x), 0 le x le 2 . Then find the number of solutions of f(f(f(x)))= (x)/(2) .

Let f(x)=2x(2-x), 0 le x le 2 . Then find the number of solutions of f(f(f(x)))= (x)/(2) .

Let f(x)=2x(2-x), 0 le x le 2 . Then find the number of solutions of f(f(f(x)))= (x)/(2) .

Let f(x)={x^(2)+k, when x>=0,-x^(2)-k, when x<0 } .If the function f(x) be continuous at x=0, then k=

Let f(x)=x^(2//3), x ge 0 . Then the area of the region enclosed by the curve y=f(x) and the three lines y=x, x=1 and x=8 is

Let f(x)=x^(2)-x-3=0 .Given f(a)=0 ; then the value of (a^(3)+1)/(a^(5)-a^(4)-a^(3)+a^(2)) equals

Let f(x)={:{(x^(2),x ge 0),(ax, x lt 0):} . Find real values of a such that f(x) is strictly monotonically increasing at x = 0 .