maddiem2523 maddiem2523

29-04-2018
Mathematics

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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))?

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sqdancefan sqdancefan

01-05-2018

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.

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