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Unformatted text preview: MAC1140: L11-13 Practice October 8, 2010 The following problems are for you to practice over the weekend. If you nish and turn them in on Monday, you will get 1 participation point for each correct problem (note: what I usually call a participation credit is 5 points; so the full sheet is worth the typical participation credit). To earn credit, you must write a full, clean solution on this paper. Do your scratchwork, etc., on another sheet, and only write on this sheet when you can write it without erasing, crossing things out, etc. For problems 1 and 2, let f (x) and g(x) be dened by the following table: x
0 1 2 3 4 i.e., f (x)
-3 2 1 5 2 g(x)
0 2 2 5 6 etc. and the range of f (0) = -3, f (1) = 2, 1. State the domain of Why or why not? f (x) g(x). Are either of f (x) and g(x) (or both) one-to-one? 2. For each of the following, evaluate if possible (if not possible, say why). (a) (f - g)(1). (b) (f g)(2). 1 (c) (g f )(3). (d) (f g)(0). 3. Let f (x) = 1 , and let x-2 g(x) = x2 + 2. (a) Find (f g)(x) and state its domain (be careful!). (b) Find (g f )(x) and state its domain. 4. Let f (x) = 3x-4 x+2 .
(if you came to my oce and showed me the general formula for the inverse of you may use it) (a) Find f -1 (x) g(x) = ax+b , cx+d 2 (b) Show that (f f -1 )(x) = x, i.e., check your work in part (a). 5. Let f (x) = 2x2 + 12x + 10. Find the: (a) Vertex. (b) Axis of symmetry. (c) x-intercepts. (d) y -intercept. (e) Domain. (f ) Range. (Hint: it may help to graph the function rst, but you do not need to include the graph) 3 ...
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