The function of `f` is continuous and has the property `f(f(x))=1-xdot` Then the value of `f(1/4)+f(3/4)` is

The function f is continuous and has the property f(f(x))=1-x for all x in [0,1] and J=int_0^1 f(x)dx . Then which of the following is/are true? (A) f(1/4)+f(3/4)=1 (B) the value of J equals to 1/2 (C) f(1/3).f(2/3)=1 (D) int_0^(pi/2) (sinxdx)/(sinx+cosx)^3 has the same value as J

The function f is continuous and has the property f(f(x))=1-x for all x in [0,1] and J=int_0^1 f(x)dx . Then which of the following is/are true? (A) f(1/4)+f(3/4)=1 (B) f(1/3).f(2/3)=1 (C) the value of J equals to 1/2 (D) int_0^(pi/2) (sinxdx)/(sinx+cosx)^3 has the same value as J

Let f(x) be a differentiable function for all x in R The derivative of f(x) is an even function If the period of f(2x) is 1 then the value of f(2)+f(4)-f(6)-f(8) is.

A finction f:R rarr R has property f(x+y)=f(x)*e^((f(y)-1)), for every x,y in R then positive value of f(4) is

If f(x) is a continuous function such that its value AA x in R is a rational number and f(1)+f(2)=6 , then the value of f(3) is equal to

Let f:(-2,2)rarr(-2,2) be a continuous function such that f(x)=f(x^(2))AA in d_(f), and f(0)=(1)/(2), then the value of 4f((1)/(4)) is equal to

If f(x) is an odd function,f(1)=3,f(x+2)=f(x)+f(2), then the value of f(3) is

A function f(x) satisfies the following property: f(x.y)=f(x)f(y). Show that the function f(x) is continuous for all values of x if it is continuous at x=1