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ex_sol(8)

# ex_sol(8) - 1 Example 5 How to ﬁnd the domain of the...

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Unformatted text preview: 1 Example 5: How to ﬁnd the domain of the inverse function f −1 ? Please follow my guidance. • Look at the graph of f (x) = a(x + 2)2 − 1 on the next page. Do you understand why the graph is half of the parabola? Please read Part 1 to see the reasoning. • After you read Part 1 to understand the graph, can you ﬁnd the range of the function f in this example? • What is the range of f ? It is the set of all the y -values of the graph of f . Since the graph of f is half of the parabola, the y -values start from the y -value of the vertex (i.e., −1). Because the x-value of the vertex (i.e., −2) is not included in the GIVEN domain (−2, ∞), then the y -value of the vertex is not included in the range of f , either. Look at the graph; it has the empty hole there. Then the range of f is (−1, ∞). • Remember that the domain of the inverse f −1 is the range of f . So, the domain of f −1 = the range of f = (−1, ∞). Then among the choices, we choose the 2nd and the last ones. Which one is the right answer? Let’s move to Part 2 of the next page. 1 2 3 2 Example 6 : 4 5 ...
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ex_sol(8) - 1 Example 5 How to ﬁnd the domain of the...

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