If `2f(xy) =(f(x))^(y) + (f(y))^(x)` for all `x, y in R` and `f(1) =3`, then the value of `sum_(t=1)^(10) f(r)` is equal to

If f(x+f(y))=f(x)+y for all x,y in R and f(1)=1, then find the value of f(10)/5,f(x) is not constant function.

If f:RtoR satisfies f(x+y)=f(x)+f(y) for all x,y in R and f(1)=7, then sum_(r=1)^(n) f(r) , is

If f:R to R satisfies f(x+y)=f(x)+f(y), for all x, y in R and f(1)=7, then sum_(r=1)^(n)f( r) is

If f(x+y)=f(x)+f(y) -xy -1 for all x, y in R and f(1)=1 then f(n)=n, n in N is true if

Let f be a function satisfying f(x+y)=f(x) *f(y) for all x,y, in R. If f (1) =3 then sum_(r=1)^(n) f (r) is equal to

If f:R rarr R satisfies f(x+y)=f(x)+f(y), for all x,y in R and f(1)=2 then sum_(r=1)^(7)f(1)

If f((x)/(y))=(f(x))/(f(y)) for all x,y in R,y!=0 and f(t)!=0, if t!=0 and f'(1)=3 then f(x) is

Consider a real-valued function f(x) satisfying 2f(xy)=(f(x))^(y)+(f(y))^(x)AA x,y in R and (1)=a, where a!=1 Prove that (a-1)sum_(i=1)^(n)f(i)=a^(n+1)-a

If (x).f(y)=f(x)+f(y)+f(xy)-2AA x,y in R and if f(x) is not a constant function,the value of f(1) is equal to