Derivatives of inverse functions

Practice the relationship between the derivatives of inverse functions:  if f and g are inverse functions, then f’(x)=1/(g’(f(x)).

Problem

Let f and g be inverse functions.
The following table lists a few values of f, g, and f, prime.
xf, left parenthesis, x, right parenthesisg, left parenthesis, x, right parenthesisf, prime, left parenthesis, x, right parenthesis
minus, 2251
5minus, 2minus, 4minus, start fraction, 1, divided by, 2, end fraction
g, prime, left parenthesis, minus, 2, right parenthesis, equals