if f(x)=√(x-1) has an inverse function, use the inverse to find (f6-1)'(2).

Question

if f(x)=√(x-1) has an inverse function, use the inverse to find (f6-1)'(2).

Answer 1

f(5) = 2 ; f^'(x) = 1/(2√(x-1)) ; f^'(5) = 1/4 ; [f^-1(5)]^' = 4

Check: f^-1(x) = x² + 1 , x ≥ 0 ; [f^-1(x)]^' = 2x ; [f^-1(2)]^' = 4