The number or linear functions `f` satisfying `f(x+f(x))=x+f(x) AA x in RR` is

The number of linear functions f satisfying f(x+f(x))= x + f (x) AA x in R is a)0 b)1 c)2 d)3

The number of linear functions of f satisfying f(x+f(x))=x+f(x) for all x in R is

The number of real linear functions f(x) satisfying f(f(x)) = x + f(x) is

Let f(x) be a function satisfying f(x) + f(x+2) = 10 AA x in R , then

Let f: R to R be a function satisfying f(2-x) = f(2+x) and f(20 -x) = f(x) AA x in R . For this functions f. answer the following If f(0) =5 then the minimum possible number of values of x satisfying f(x)= 5 for x in [0,170] is