If `f(x+y)=f(xy)AAx,y in R` then prove that `f` is a constane function.

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

If f(x+y)=f(x)+f(y),AAx ,\ y in R then prove that f(k x)=kf(x)for\ AAk ,\ x in Rdot

A function f:R rarr R satisfies that equation f(x+y)=f(x)f(y) for all x,y in R ,f(x)!=0. suppose that the function f(x) is differentiable at x=0 and f'(0)=2. Prove that f'(x)=2f(x)

Statement 1: Let f: R -> R be a real-valued function AAx ,y in R such that |f(x)-f(y)|<=|x-y|^3 . Then f(x) is a constant function. Statement 2: If the derivative of the function w.r.t. x is zero, then function is constant.

Statement 1: Let f: R -> R be a real-valued function AAx ,y in R such that |f(x)-f(y)|<=|x-y|^3 . Then f(x) is a constant function. Statement 2: If the derivative of the function w.r.t. x is zero, then function is constant.

A function f:R rarr R satisfies the equation f(x+y)=f(x)f(y) for all x,y in R.f(x)!=0 Suppose that the function is differentiable at x=0 and f'(0)=2. Prove that f'(x)=2f(x)

A function f:R rarr R satisfies the equation f(x+y)=f(x)f(y) for all x,y in R , f(x) ne 0 . Suppose that the function is differentiable at x=0 and f'(0)=2. Prove that f'(x)=2f(x).

Statement 1: Let f: RvecR be a real-valued function AAx ,y in R such that |f(x)-f(y)|<=|x-y|^3 . Then f(x) is a constant function. Statement 2: If the derivative of the function w.r.t. x is zero, then function is constant.

Statement 1: Let f: RvecR be a real-valued function AAx ,y in R such that |f(x)-f(y)|<=|x-y|^3 . Then f(x) is a constant function. Statement 2: If the derivative of the function w.r.t. x is zero, then function is constant.