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

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: RvecR be a continuous function which satisfies f(x)= int_0^xf(t)dtdot Then the value of f(1n5) is______

If f(x) is continuous and int_(0)^(9)f(x)dx=4 , then the value of the integral int_(0)^(3)x.f(x^(2))dx is

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.

Let f: R->R be a continuous function and f(x)=f(2x) is true AAx in Rdot If f(1)=3, then the value of int_(-1)^1f(f(x))dx is equal to (a)6 (b) 0 (c) 3f(3) (d) 2f(0)

A continuous, even periodic function f with period 8 is such that f(0)=0,f(1)=-2,f(2)=1,f(3)=2,f(4)=3, then the value of tan^(-1) tan{f(-5)+f(20)+cos^(-1)(f(-10))+f(17)} 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________

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

Suppose f is a real function satisfying f(x+f(x))=4f(x)a n df(1)=4. Then the value of f(21) is 16 21 64 105

If f is a real valued function such that f(x+y) = f(x) + f(y) and f(1)=5, then the value of f(100) is