A real valued function f (x) satisfies the functional equation f (x-y)=
` f(x) f(y) - f(a-x) f(a +y) ` where a is a given constant and f (0) =1, f(2a -x) is equal to

The function f Satisfies the functional equation 3 f (x) +2f ((x+59 )/(x-1))=10 x +30 for all real x ne 1 . The value of f (7) is

A function f: R -> R satisfy the equation f (x)f(y) - f (xy)= x+y for all x, y in R and f(y) > 0 , then

A function y=f(x) satisfies the differential equation (d y)/(d x)+x^2 y=-2 x, f(1)=1 . The value of |f^( prime prime)(1)| is

If for a function f : R to R f (x +y ) =F(x ) + f(y) for all x and y then f(0) is

A function f (x) is defined for all x in R and satisfies, f(x + y) = f (x) + 2y^2 + kxy AA x, y in R , where k is a given constant. If f(1) = 2 and f(2) = 8 , find f(x) and show that f (x+y).f(1/(x+y))=k,x+y != 0 .

If function f satisfies the relation f(x)*f^(prime)(-x)=f(-x)*f^(prime)(x) for all x ,

Determine the function satisfying f^2(x+y)=f^2(x)+f^2(y)AAx ,y in Rdot

Let y=f(x) be a function satisfying the differential equation (x d y)/(d x)+2 y=4 x^2 and f(1)=1 . Then f(-3) is equal to

If f (x/y)= f(x)/f(y) , AA y, f (y)!=0 and f' (1) = 2 , find f(x) .

Consider the real function f(x ) = ( x+2)/( x-2) prove that f(x) f(-x) +f(0) =0