Question

Suppose you have a function y = f(x) such that the domain of f(x) is 1 ≤ x ≤ 6 and the range of f(x) is −2 ≤ y ≤ 5. (a) what is the domain of f(3(x − 2))?

Answer 1

The function f(z) is defined for z in [1, 6]. We want to find x such that
  z = 3(x -2)
Substituting the interval for z, we have
  [1, 6] = 3(x -2)
  [1/3, 2] = x -2 . . . . divide by 3
  [2 1/3, 4] = x . . . .. add 2

The domain of f(3(x -2)) is ...
  2 1/3 ≤ x ≤ 4.