If `f(x)` satisfies the relation `f((5x-3y)/2)=(5f(x)-3f(y))/2AAx ,y in R ,` and `f(0)=3a n df^(prime)(0)=2,` then the period of `"sin"(f(x))` is (a)`2pi` (b) `pi` (c) `3pi` (d) `4pi`

If f((x+2y)/3)=(f(x)+2f(y))/3\ AA\ x ,\ y in R and f^(prime)(0)=1 , f(0)=2 , then find f(x) .

Let f(x+y)=f(x)f(y) for all x and y . Suppose f(5)=2 and f^(prime)(0)=3 , find f^(prime)(5) .

If f(x) is a function satisfies the relation for all xy in R,f(x+2y)-f(x)+f(2y) and If f'(0)=3 and function is differentiable every where,then find f(x)

If the function / satisfies the relation f(x+y)+f(x-y)=2f(x),f(y)AA x,y in R and f(0)!=0 ,then f(x) is an even function f(x) is an odd function If f(2)=a, then f(-2)=a If f(4)=b, then f(-4)=-b

if f(x)=sin((pi)/(3)[x]-x^(2)) then the value of f((sqrt(pi))/(3)) is

If f'(x)=a sin x+b cos x and f'(0)=4,f(0)=3,f((pi)/(2))=5f(x)

f(x+y)=f(x)*f(y) for all x,y anf f(5)=2,f'(0)=3 then f(5) will be

The period of f(x)=(sin(pi x))/(2)+2(cos(pi x))/(3)-(tan(pi x))/(4) is