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# Review Sheet for MATH 1330 at UH

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This 3 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 27 views.

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Date Created: 02/06/15

Exercise Set 14 Operations on Functions Answer the following using the graph below The following method can be used to nd the domain of fog a Find the domain of g b Find f o g c Look at the answer from part b as a stand alone function ignoring the fact that it is a composition of functions and find its domain d Take the intersection of the domains found in steps a and c This is the domain offog Note We check the domain of g because it is the inner 17 a g2 b fg2 c fa d gf2 function offog ie fgx Ifan xvalue is not in the domain of g then it also can not be an 18 a g0 b fg0 inputvalue for fog c f0 d gf0 Use the above steps to find the domain of f o g for the 19 3 f0g 3 13 golf 3 following problems 20 a foglil b goX71 1 21 a f f3 b gogxiz 33 fx g0 5 22 a f f5 b gogxis 1 23 a fogX4 b goX4 34 fx g0 2 24 a fog 5 b fogXZ 35 fx x274 gxJ 6 Use the functions f and g given below to evaluate the following expressions 5 36 fx x272 gxv3x fx372x and gxx275x4 25 a go b fg0 c M d gf0 For each of the follow1ng problems 26 a gel b fg71 a Find fog and its domain c fil d gf1 b Find go f and its domain 27 a foglil b gofXJ 37 fxx23xgx2x77 28 a f g4 b gof4 38 fx6x 2 x77x2 29 a f f6 b gogxs g 30 a fof4 b gogX74 39 fxx2gx 4 31 a fogXx b goXx 40 fx J33 gxx2 32 a fofx b gogXx Math 1330 Precalculus The University of Houston Chapter I A Review QfFunctions Exercise Set 14 Operations on Functions 41 42 fxJx739 gx757x fxl3x gx92x Answer the following 43 44 45 46 47 48 Given the functions f x x2 2 and gx 5x78 find a fg1 b gf1 c fgx d gfx e ff1 t gg1 g ffx h ggx Given the functions f x x 1 and gx 3x7 2x2 find a fg3 b gf3 C fg X d gfx e ff3 i gg3 g ffx h ggx Given the functions f x and gx 5 find a fg2 b gf2 C fgx d gfx Given the functions f x 2X and x 5 x find got 71 lt a fg3 b gf3 C fgx d gfx Given the functions x x2 71 gx 3x7 5 and hx 17 2x find b ghf3 a fgh2 C f g h d gohof Given the functions x 2x2 3 gx x 4 and hx 3x 7 2 find b ghf1 a fgh1 C fogoh d gohof Math 1330 Precalculus The University of Houston 49 Given the functions x x2 4 gx Jx 3 and hx 2x 1 find a hfg4 C f ogoh b fgh0 d hofog 50 Given the functions fx 2 gx1 72 andhx374x find 1 a hfg5 C f ogoh b fghe 2 d hofog Functions f and g are defined as shown in the table below 0 124 x fx 2 4 7 00 4 5 0 Use the information above to complete the following tables Some answers may be unde ned 51 52 53 54 0124 Chapter I A Review QfFunctions Exercise Set 14 Operations on Functions Answer the following For each of the following problems a Find f g and its domain b Find f g and its domain c Find fg and its domain d Find L and its domain g 1 Notefor ad39 Do not sketch any graphs 3 27 7 2 Find f73g73 2x3 gx x 4x 12 b Find f0 g0 4 fx 2 75x gx x2 8x15 c Find f76 g76 3 X d Find f5g5 5 WE g 2 e Find f7 g7 4 2x 6 f X EU 1 Sketch the graph of f g Hint For any x x75 x75 value add the y values offand g g Whatis the domain of fg7Explainhow 7 fxquot 76quot go 07quot you obtained your answer 8 fx42x73 gxlx4 9 fxIx279 gxlx24 10 fx 497x2 gxx73 Find the domain of each of the following functions 11 fx 2 x71 x 7 3 a Find f72 7 g72 12 hog J77 b Find f0 7 g0 X c Find f747g74 13 got 3 7 7 xi d Find mega x7 quot7 9 Find f4 g4 14 fx il7 X X i 1 Sketch the graph of f7 g Hint For any x value subtract the y values of f and g 15 mo quot 2 g What is the domain of f7 g 7 Explain how x75 you obtained your answer 16 gx x 7 3 x71 Math 1330 Precalculus The University of Houston Chapter I A Review QfFunctions

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