Derivative Inverse Domain and Range Problem

Question

Consider the function  f(x) = 9/(x-4) for x > 4

f^-1 = 5

(f^-1)'(5) = ?????

Calculate and state domain and range of f^-1

Use interval notation.

f^-1(x) = (9/x) + 4

domain = ???

range = ????

Answer 1

f(x) = 9/(x - 4);

Domain f(x): x > 4, Range f(x) = (0, ∞);

y = 9/(x - 4); x = 9/(y - 4); y = 9/x + 4

f^-1(x) = 9/x + 4; f^-1(5) = 9/5 + 4 = 29/5

Domain f^-1(x): (0, ∞). Range f^-1(x): (4, ∞)