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Unformatted text preview: .) (c) Find a formula for the inverse function of f . 3. Simplify the following expressions. (a) tan(arcsin x ) (b) cos(2 arctan x ) (Hint: Note that arcsin x = sin-1 x , and arctan x = tan-1 x . See Example 13 on p. 69.) 1 4. State the domains of the following functions and sketch their graphs. (a) f ( x ) = sin(arcsin x ) (b) g ( x ) = arcsin(sin x ) (Hint: For g ( x ) , note that it has period 2 . If you can draw its graph on the interval [-, ] , then you can just replicate the rest of the graph from the piece you have.) 5. Let f be a one-to-one function. For each question below, if your answer is yes, give a short proof, and if your answer is no, give an example where the statement fails. (a) Is f always either increasing or decreasing? (b) If f is increasing, is f-1 also increasing? (c) If f is decreasing, is f-1 also decreasing? (d) If f is odd, is f-1 also odd? 2...
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- Spring '10
- Inverse function, correct drop box