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.

Let f(x) be real valued and differentiable function on R such that f(x+y)=(f(x)+f(y))/(1-f(x)dotf(y)) f(0) is equals a. 1 b. 0 c. -1 d. none of these

Let f(x) be real valued and differentiable function on R such that f(x+y)=(f(x)+f(y))/(1-f(x)dotf(y)) f(x) is Odd function Even function Odd and even function simultaneously Neither even nor odd

Let f: R->R be a differentiable function with f(0)=1 and satisfying the equation f(x+y)=f(x)f^(prime)(y)+f^(prime)(x)f(y) for all x ,\ y in R . Then, the value of (log)_e(f(4)) is _______

Suppose f: R->R^+ 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 a. 6 b. 9 c. 12 d. 15

Let f: R → R be a one-one onto differentiable function, such that f(2)=1 and f^(prime)(2)=3. Then, find the value of (d/(dx)(f^(-1)(x)))_(x=1)

Let f : R to R be a function such that f(x)=x^3+x^2+3x+sinx . Then

Let f be a real-valued differentiable function on R (the set of all real numbers) such that f(1)=1. If the y- intercept of the tangent at any point P(x , y) on the curve y=f(x) is equal to the cube of the abscissa of P , then the value of f(-3) is equal to________

Let f : R to R be a function such that f(0)=1 and for any x,y in R, f(xy+1)=f(x)f(y)-f(y)-x+2. Then f is

Let f:R to R be defined by f(x)=x|x| , then the function f is -

Let f:R to R be a differentiable function and f(1)=4 and f'(1)=2 , then the value of lim_(x to 1) int_(4)^(f(x))(2t)/(x-1)dt is -