If `f(x+y)=f(x)*f(y),AA x , y in R ,f(0)=1 and g(x)=f(x)/(1+(f(x))^2` such that `g(5)=7.` Then the value of `g(-5)` is equal to

If f(x+y)=f(x)f(y)AA x,y in R, f(0) ne 0 then F(x) = {f(x)/(1+(f(x)))^2 is

If f(x + y) = f(x) f(y) AA x, y and f(5) = 2, f'(0) = 3 then f'(5) =

f(x)=x^(2)-2x,x in R, and g(x)=f(f(x)-1)+f(5-f(x)) Show that g(x)>=0AA x in R

Let f(x+y)=f(x)f(y)AA x, in IR, f(6)=5 and f'(0)=1 . Then the value of f' (6) is

Let f:R rarr R be a function which satisfies f(x+y)=f(x)+f(y) AA x, y in R . If f(1)=2 and g(n)=sum_(k-1)^((n-1))f(k),n in N then the value of n , for which g(n)=20 , is :

f((x)/(y))=f(x)-f(y)AA x,y in R^(+) and f(1)=1, then show that f(x)=In x

If (x+f(y))=f(x)+y AA x,y in R and f(0)=1 then find the value of f(7).

Let f be a differentiable function satisfying f(xy)=f(x).f(y).AA x gt 0, y gt 0 and f(1+x)=1+x{1+g(x)} , where lim_(x to 0)g(x)=0 then int (f(x))/(f'(x))dx is equal to