Question

For each of the given functions f(x) , find the derivative (f^-1)'(c) at the given point c , first finding a = f^-1(c)



f(x) = 3x+7x^15 ; c = -10
a = -1

(f^-1)'(c) = ????



f(x) = x^2 - 15x + 77 on the interval [7.5, infinity); c=23
a = ????

(f^-1)'(c) = ????

Answer 1

if f(a) = b, then (f^-1)'(b) = 1/f'(a)
so, since f(-1) = -10
(f^-1)'(-10) = 1/f'(-1) = 1/108

x^2 - 15x + 77 = 23
x = 6 or 9
But only 9 is in the domain.
So, (f^-1)(23) = 1/f'(9) = ____