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 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

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

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 f (x) = (x + 1)/(x - 1) is a real function , x ne 1 , then f [f(2)] is . . . .

Consider the real function f(x) =1 -2x find x if f(x) =-1

Let f: R->R be a differentiable function with f(0)=1 and satisfying the equation f(x+y)=f(x)f^(prime)(y)+f^(prime)(x)f(y) for all x ,\ y in R . Then, the value of (log)_e(f(4)) is _______

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

Consider the real function f(x) =1 -2x find f(-1) and f(2)

Let R be the set of reals . Define a function F : R to R by f (x) = 2x^2-1 find f(f(x))