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Unformatted text preview: ction 4.2, graph y = f (x). Verify f is oneto-one on the interval (−1, 1). Use the procedure outlined on Page 299 and your graphing calculator to find the formula for f −1 (x). Note that since f (0) = 0, it should be the case that f −1 (0) = 0. What goes wrong when you attempt to substitute x = 0 into f −1 (x)? Discuss with your classmates how this problem arose and possible remedies. 6. Suppose f is an invertible function. Prove that if graphs of y = f (x) and y = f −1 (x) intersect at all, they do so on the line y = x. 7. With the help of your classmates, explain why a function which is either strictly increasing or strictly decreasing on its entire domain would have to be one-to-one, hence invertible. 8. Let f and g be invertible functions. With the help of your classmates show that (f ◦ g ) is one-to-one, hence invertible, and that (f ◦ g )−1 (x) = (g −1 ◦ f −1 )(x). 9. What graphical feature must a function f possess for it to be its own inverse? 310 5.2.2 Further...
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