Let `f` be a function such that `f((8)/(sqrt(1+sqrt(x))))=x` for all `x>=0` .The value of `f(4)` equals

Let f be a function such that f(3)=1 and f(3x)=x+f(3x-3) for all x. Then find the value of f(300).

Let f(x) be a continuous function such that f(a-x)+f(x)=0 for all x in [0,a] . Then, the value of the integral int_(0)^(a) (1)/(1+e^(f(x)))dx is equal to

Let f(x) be a function such that :f(x-1)+f(x+1)=sqrt(3)f(x), for all x varepsilon R. If f(5)=100, then prove that the value of sum_(r=o)^(99)f(5+12r) will be equal to 10000.

Let X be the set of all positive integers greater than or equal to 8 and let f:X rarr X be a function such that f(x+y)=f(xy) for a>=4,y>=4, If f(8)=8, then the value of f(20) is

If function f(x)=(sqrt(1+x)-3sqrt(1+x))/(x) continuous function at x=0 then f(0) is equal to

[" Let "f(x)" be a function such that "],[f''(x)=f(x)" and "f'(0)=f(0)=0" .The "],[" value of "(f(x))/(4-f(x))dx" is equal to "]

If a function fis such that f(x)=int_(0)^(x)(dx)/(f(x)) and f(1)=sqrt(2), then the value of f(2) is

Statement -1: Let f(x) be a function satisfying f(x-1)+f(x+1)=sqrt(2)f(x) for all x in R . Then f(x) is periodic with period 8. Statement-2: For every natural number n there exists a periodic functions with period n.

Let f be a differentiable function such that f(0)=e^(2) and f'(x)=2f(x) for all x in R If h(x)=f(f(x)) ,then h'(0) is equal to