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) 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

If f(x) = (x + 1)/(x-1) , then the value of f{f(3)} is :

Let f be a function satisfying the functional rule 2f(x)+f(1-x)=xAAx in Rdot Then the value of f(1)+f(2)+f(3) is

Let f(x) be continuous functions f: RvecR satisfying f(0)=1a n df(2x)-f(x)=xdot Then the value of f(3) is 2 b. 3 c. 4 d. 5

Let f(x) be continuous functions f: RvecR satisfying f(0)=1a n df(2x)-f(x)=xdot Then the value of f(3) is 2 b. 3 c. 4 d. 5

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

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

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

A function is defined as f(x)=x^2-3xdot Find the value of f(2)dot Find the value of x for which f(x)=4.

If f is continuous on [0,1] such that f(x)+f(x+1/2)=1 and int_0^1f(x)dx=k , then value of 2k is 0 (2) 1 (3) 2 (4) 3