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The Humongous Book of Trigonometry Problems by W. Michael Kelley

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Graphs of Inverse Trigonometric Functions

Including domain and range

9.1    The graph of a function f(x) passes through points (–2,6), (0,3), and (4,–9) and has inverse function f–1(x). Identify three points through which the graph of f–1(x) passes.

If f(x) passes through points (–2,6), (0,3), and (4,–9), then –2, 0, and 4 are members of the domain and 6, 3, and –9 are members of the range. Specifically, f(–2) = 6, f(0) = 3, and f(4) = –9. To identify points on the inverse function f–1(x), reverse the numbers in the ordered pair.

If a number is a member of the domain, you can plug it into the function and get some real number output. Members of the range are outputs of the function.

Thus, f–1(x) passes through points (6,–2), (3,0), and (–9,4). ...

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