Answer to Question #104827 in Calculus for SHIVAM KUMAR

Question

if f is one - one onto and differentiablw on R, then (f^-1)'(6)=1/f'(6) .Is the statement tue or false.
Explain why

Answer 1

if f is one - one onto and differentiablw on R, then, $(f^{-1}(6))^{'}=1/f^{'}(6)$ is true because $(f^{-1}(y_o))^{'}=1/f^{'}(x_o)$ for $f(x)=x$ .