Question

the table above gives values of the differentiable functions f and g, and f', the derivative of f, at selected values of x. if g(x) = f-1(x), what is the value of g'(4)?

Answer 1

Check your given table for the value of x such that f(x) = 4. Then x = g(4), and by the inverse function theorem,

$g'(4) = \dfrac1{f'(x)} = \dfrac1{f'(g(4))}$