If `f'(x) = x -(3)/(x^2). F (1) = (11)/(2), ` find f(x)

If f'(x)=x^2-1/x^2 and f(1)=1/3 , find f(x).

if f'(x) = 3x^2-2/x^3 and f(1)=0 , find f(x).

If f'(x)=x/2 + 2/x and f(1)=5/4 , then find f(x) .

If f(x) = (x -2)/(x-3), x ne 3 , Examine whether f(x) is invertible or not. If f(x) is invertible, then find f^-1 (x) .

If f((xy)/(2)) = (f(x).f(y))/(2), x, y in R, f(1) = f'(1)."Then", (f(3))/(f'(3)) is.........

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...... .

Let f(x)=x^3-3x^2+2x Find f'(x)

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

If f(x) = x^2 , find (f(1.1)-f(1))/((1.1-1)) .