Question

The function f is defined by f(x) = -x³-3x - 5 and the point (1,-9) is on the graph of f. If

G(x) = f^-1(x), what is the value of g'(-9)?

Answer 1

Explanation:

We have g'(-9) = 1/{f'[f^-1(-9)]}

= 1/[f'(1)]

= -1/6.

(*): f(x) = -x³ - 3x - 5, f'(x) = -3x² - 3, f'(1) = -6.