Math 155 Sept. 7 Notes
Math 155 Sept. 7 Notes Math 155
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This 4 page Class Notes was uploaded by Hanna Markezich on Friday September 11, 2015. The Class Notes belongs to Math 155 at Northern Illinois University taught by Vobornik in Fall 2015. Since its upload, it has received 53 views. For similar materials see Trigonometry and Elementary Functions in Mathematics (M) at Northern Illinois University.
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Date Created: 09/11/15
Homework 3 and Quiz 3 due Tuesday September 15 at 1159 PM Section 61 Composition of Functions Definition Given two functions f and g the composite function denoted by f0 g i defined by f0 gX fgX NOTE Always use the function next to x first then insert into the second func on The domain is the set of all numbers in the domain of 9 such that gx is in the domain of f Example fltxgtx2 gxgt 1 Domain of f Domain of g xlxa 2 xlxa 1 1 f0 gX 2FMddomam f0 gX 1 x4112 This is a complex fraction to simplify multiply top and bottom by denominator of mini fraction 1 1 2 1gt x l 42x 1 x l x l 42x 2 2x2 Domain offogx x 11 Check g1 i i2 2 lt Domain of fx Section 62 Inverses Properties of Inverse 1 Domain of fx Range of f391x lt inverse 2 Range of fx Domain of f391x 3 fo f391x x lt identity function 4 f391o fx x lt identity function 5 graphs are symmetric to yx Example fltxgt 3 x 1 x1 IS onetoone over It domain x x 1 range x X79 3 Find the inverse 1 replace fx with y 3x1 x l 2 SWITCH Make all x s gt y s and make y s gt x s 3y1 y 3y1 solve for y y1x y 1 lt cear all functions yx x 3y1 lt get yterms on one side yx 3x 1x lt factor out yx 3 1x lt divide 99 9 7 y 1 xinverse Dxx 3Rxxa 1 x 3 Does it work 3 2 1 f2 U 7I 2 1 1 f 17 V 7 3 4 Example 1 x l fiofgtltxgt 3 31 1x 13x1 x 13x1 4x X 3x1 3x 1 3x1 3x3 4 Section 63 Exponential Functions Definition an exponential function is a function of the form fxAX variable is the exponentA gt 0 A79 1 Abase Example fx2X A2 x fx2X 0 201 1 212 2 224 3 238 1 1 391 1 2 21 2 1 1 2 2 2 22 4 1 1 3 3 2 23 8 Properties when Agt1 1 Domain oooo 2 Range 0 00 lt positive numbers only 3 No xintercept yintercept at 01 4 HA at yO 5 graph is smooth and continuous 6 Always increasing 7 onetoone function has inverse Properties when Olt A lt1 Domain oooo Range 0 00 lt positive numbers only No xintercept yintercept at 01 HA at yO Always decreasing graph is smooth and continuous onetoone function has inverse NFDSN P NE
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