Question

The table below gives selected values for the differentiable and decreasing function f and it’s derivative. If f^-1(x), what is the value of g’(9)

Answer 1

According to the table, f(x) = 9 when x = -5. So if g(x) is the inverse of f(x), it follows that g(9) = -5.

By the inverse function theorem,

$g'(9) = \dfrac1{f'(g(9))} = \dfrac1{f'(-5)} = \boxed{-\dfrac14}$