`f:R to R` such that `f(x+f(x))=4f(X)` and `f(1)=4`. What is the value of `f(5)` ?

Suppose f is a real function satisfying f(x+f(x))=4f(x) and f(1)=4. Then the value of f(21) is 162164105

Let f: R rarr R be a function such that f(2)=4 and f'(2)=1 . Then, the value of lim_(x rarr 2) (x^(2)f(2)-4f(x))/(x-2) is equal to

If f(x) is a function such that f(x-1)+f(x+1)=sqrt(3)f(x) and f(5)=10 then the sum of digit of the value of sum_(r=0)^(19)f(15+12r) is

If 5f(x)+4f((1)/(x))=x-1,x!=0 then write the value of 9f(2)

Let f:R to R be continuous function such that f(x)=f(2x) for all x in R . If f(t)=3, then the value of int_(-1)^(1) f(f(x))dx , is

f(x) is a polynomial function, f: R rarr R, such that f(2x)=f'(x)f''(x). The value of f(3) is