I figured out that the question can be solved as the following :
point A(α,β) on the function f(x) curve
point A^'(β,α) on the function f^(-1)(x)
So the slope of tangent to the f^(-1) curve is :
d/dx f^(-1)(β) = 1/d/dxf(α)
And the slope of normal line to the curve is as :
Please comment me if you agree with me.