Find all functions F(x) and G(x) which satisfy the system: `F(2x+1)+2G(2x+1)=2x` and `F(x/(x-1))+G(x/(x-1))=x`

Suppose that the function f(x) and g(x) satisfy the system of equations f(x)+3g(x)=x^(2)+x+6 and 2f(x)+4g(x)=2x^(2)+4 for every x. The value of x for which f(x)=g(x) can be equal to

Suppose that the function f(x) and g(x) satisfy the system of equations f(x)+3g(x)=x^(2)+x+6 and 2f(x)+4g(x)=2x^(2)+4 for every x. The value of x for which f(x)=g(x) can be equal to

The function f, g and h satisfy the relations f'(x)=g(x+1)andg'(x)=h(x-1) . Then, f''(2x) is equal to

If f(x) is an even function and g(x) is an odd function and satisfies the relation x^(2)f(x)-2f(1/x) = g(x) then

f(x)=(1+x) g(x)=(2x-1) Show that fo(g(x))=go(f(x))

If the function f(x) = x^3 + e^(x/2) and g(x) =f^-1(x) , then the value of g'(1) is

If the function f(x)=x^3+e^(x/2) and g(x)=f ^(−1)(x) , then the value of g ′ (1) is

If f(x), g(x) be twice differentiable functions on [0,2] satisfying f''(x) = g''(x) , f'(1) = 2g'(1) = 4 and f(2) = 3 g(2) = 9 , then f(x)-g(x) at x = 4 equals (A) 0 (B) 10 (C) 8 (D) 2