Given `f(g(x))=1+x-2x^(2)+5x^(3)` and `f(x)=1+3x AA x in R`, then the value of `3g(1)` is equal to

If f(x)=x^(3)+3x+1 and g(x) is the inverse function of f(x), then the value of g'(5) is equal to

If a function f(x) satisfies the relation 3f(x)-5f((2)/(x))=3-x+x^(2)AA x in R-{0} ,then the value of f(1) is equal to

If f(x)=x^(2)g (x) and g(1)=6, g'(x) 3 , find the value of f' (1).

Let f: R rarr R defined by f(x)=x^(3)+3x+1 and g is the inverse of 'f' then the value of g'(5) is equal to

Let f(x)=[x] and g(x)=|x|, AA x epsilon R then value of gof((-5)/3)+fog((-5)/3) is equal to : (where fog(x)=f(g(x)))

Let f:R rarr R be defined by f(x)=x^(3)+3x+1 and g be the inverse of f .Then the value of g'(5) is equal to

If the function f (x)=-4e^((1-x)/(2))+1 +x+(x ^(2))/(2)+ (x ^(3))/(3) and g (x) =f ^(-1)(x), then the value of g'((-7)/(6)) equals :

Let f_(1) (x) and f_(2) (x) be twice differentiable functions where F(x)= f_(1) (x) + f_(2) (x) and G(x) = f_(1)(x) - f_(2)(x), AA x in R, f_(1) (0) = 2 and f_(2) (0) = 1. "If" f'_(1)(x) = f_(2) (x) and f'_(2) (x) = f_(1) (x) , AA x in R . then the number of solutions of the equation (F(x))^(2) =(9x^(4))/(G(x)) is...... .