If f is a one to one function with f(8)=3 and f'(8)=5 what is the value of (f^-1)'(3)

Answer 1

Since f(8) = 3, (8,3) is on the graph of y = f(x) and (3,8) is on the graph of y = f^-1(x).

The slope of the tangent line to the graph of y = f^-1(x) at the point (3,8) is the reciprocal of the slope of the tangent line to the graph of y = f(x) at the point (8,3).

So, (f^-1(3))' = 1 / f'(8) = 1/5