Worksheet_7_Solutions

# Worksheet_7_Solutions - S’O/LL {Vb/73 MATH 110 Worksheet...

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Unformatted text preview: S’O/LL {Vb/73 MATH 110 Worksheet 7 October 15, 2009 Review of Inverse Functions 1. Find f‘1(y), f‘1(4), and the domain and range off—1(3)) for the following functions. a. f(x)=3x+4 Pt'x)=3x#‘l=j T" (431(‘4—‘0/g ‘-0 ‘gx :j—H . dcmaim=rczn3¢ —— (-00:90) x = (5—6012 = 979 b. f(x) = 5x u 21 gm = sx—ll = 5 §"(“—l) = (HVZUIS‘ : § 9‘ x = fj ‘1 11 x' : ("TWO/4’ - 9"(51') Section 3.2 Logarithms as lnverses of Exponentiation chML‘l'lnaZVﬂtﬁﬁ a =— (7- 00/40) Understand the deﬁnition of the logarithm with an arbitrary base: 2. Evaluate theindicated expressions. x 3. [092123 at 9'0 2, =li2\$5 smut m? b. 10923-35 ﬁx 5:: 2" =12: cpr X="7’ c. 10982 :x' So 3" =2, ﬁnal-L 2g"— 1/3 d. Find a numbertsuch that log t = 8 . x . , 2 2 = t Sc. t = 296 e. Findanumbertsuchthatlogzt=—9. _,q A y 2:5 So t= 5:2. 3. Find a number b such that the indicated equality holds. a. £0=éq so b- mm 5 '5"? e 5417‘” =2, 50 3311 531 c. Find a numberx such that 1094 (3x + 1) = —2 . - R. ‘l “‘BXH ____l__. :gx‘il Hp .i__| 53X lLa -—l.s: 23x K3“;- Understand the consequences of thinking of logarithms as inverse functions: 4. Find a formula for the inverse function f “101‘ the Indicated function f. a. f (x) = 4.7x BU cit-Ruben, g'wj') " 103%.? fj El 3:] qu‘ﬁ‘rLiHvl’L, k"/-j)'% C f(x)= x-3 5K- : _ §‘=jg+g so [Ojg(!ji3)=>< ‘5”(5) d. f(x)=8—91092(4x—7) _ — __ *3 8-9|051(cfx_-;) :5 f |031(’—tx-?)- chi _‘:1 [3.131 (foe}) ; a ._ g (3—57/53 W 5. Find a formula for fog(x) for the given functions. 3- f (x) = logsx and g(x) = 53+2x . A, K _ — 2A ‘ Sow—H 5” ) : mas-L5“ )= 5+2 >< b‘ ﬁx) = 53+” and 90‘) = logsfzio- x 3 1193-5" 3 105 7x ->_ 59:5(ingx): 5 35' =5'S :5-(‘52L 5)L c. Find a numbermsuch that logsaogem) = 3 my 3 5g ' X 5 ’29 5'37 I03 15 m. L— "'"‘> IRSF=)D¢JkrVL '9 (‘9 :m 6. Epr-ein vvhy {093100 is between 4 and 5. s - 5 . 1063'00” -‘> 3":100 . We ram 3411‘s] 4 ID'C A % ‘t 1‘43 w So 4<K¢§ . Be able to evaluate logarithms in simple cases: 7. Evaluate the following. 3. 1091101000 1% a ‘0 = 1000 —-o x Z 3 1 — . “x '4 : _.\—— “'9 T. —_L_ b. logic-10R -‘ K —9 IL» lace K 5 x f '2 c. log28 = x —> :2 ' '5 ’7 x t: d. [09381 = x —" ...
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Worksheet_7_Solutions - S’O/LL {Vb/73 MATH 110 Worksheet...

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