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


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
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, p, i or 2, slash, 3, space, p, i