Determine the function satisfying `f^2(x+y)=f^2(x)+f^2(y)AAx ,y in Rdot`

If f is polynomial function satisfying 2+f(x)f(y)=f(x)+f(y)+f(x y)AAx , y in R and if f(2)=5, then find the value of f(f(2))dot

If f is polynomial function satisfying 2+f(x)f(y)=f(x)+f(y)+f(x y)AAx , y in R and if f(2)=5, then find the value of f(f(2))dot

f:R^+ ->R is a continuous function satisfying f(x/y)=f(x)-f(y) AAx,y in R^+ .If f'(1)=1,then (a)f is unbounded (b) lim_(x->0)f(1/x)=0 (c) lim_(x->0)f(1+x)/x=1 (d) lim_(x->0)x.f(x)=0

Consider a real-valued function f(x) satisfying 2f(x y)=(f(x))^y+(f(y))^xAAx , y in Ra n df(1)=a ,w h e r ea!=1. Prove that (a-1) sum_(i=1)^nf(i)=a^(n+1)-a

If f is a function satisfying f (x +y) = f(x) f(y) for all x, y in N such that f(1) = 3 and sum _(x=1)^nf(x)=120 , find the value of n.

Let f: RvecR be a function satisfying condition f(x+y^3)=f(x)+[f(y)]^3 for all x ,y in Rdot If f^(prime)(0)geq0, find f(10)dot

If the function / satisfies the relation f(x+y)+f(x-y)=2f(x),f(y)AAx , y in R and f(0)!=0 , then (a) f(x) is an even function (b) f(x) is an odd function (c) If f(2)=a ,then f(-2)=a (d) If f(4)=b ,then f(-4)=-b

Consider the function f(x) satisfying the relation f(x+1)+f(x+7)=0AAx in Rdot STATEMENT 1 : The possible least value of t for which int_a^(a+t)f(x)dx is independent of ai s12. STATEMENT 2 : f(x) is a periodic function.

Suppose f: RvecR^+ be a differentiable function such that 3f(x+y)=f(x)f(y)AAx ,y in R with f(1)=6. Then the value of f(2) is 6 b. 9 c. 12 d. 15