Exercise 26 which of the following functions are one

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Exercise 26Which of the following functions areone-to-one? Justify your answers.(a)f(x) =x3+ 1(b)f(x) =x(x2) + 1(c)f(x) =x3x(d)f(x) =ax2, wherea= 0Exercise 27Find the inverse of each of the followingfunctions.(a)f(x) =(1x)3(b)f(x) = 51x(c)f(x) =15xExercise 28For each of the following functionsf, find theinverse functionf1, and sketch the graphoff1.(a)f(x) = 23x(b)f(x) = 2x+ 2(x(1,2))Exercise 29Consider the functionf(x) =x24x+ 7.(a) Complete the square in the rule off.(b) Sketch the graph off.(c) Using your sketch, specify a one-to-onefunctiongthat is a restriction offandhas the same image set asf.(d) Find the inverse functiong1ofg.Pair each exponential function below with itsapproximately equivalent form. (Try to dothis without using a calculator.)(a)f(x) = 1000x(b)f(x) = 0.5x(c)f(x) =e6.907 755x(d)f(x) = 2.718 282x(e)f(x) =e0.693 147x(f)f(x) =exExercise 31Find the exact value of each of the followingexpressions, without using your calculator.(a) log31(b) log5(125)(c) ln(e3.1)(d) log10(1000)(e)eln 4(f) 23 log25Exercise 32For each of the following equations, find thevalue ofxthat satisfies it, if there is such avalue.(a) 3 = log5x(b)x= log2(2)(c)12= logx9(d)x= log112Exercise 33Find the exact value of the expressioneln 2+ log51125+ ln(4e)ln 4,without using your calculator.Exercise 34For each of the following functions, describehow you could obtain its graph by applyingscalings and translations to the graph of thefunctionf(x) =ex, and sketch the graph ofthe function.(a)g(x) =ex1+ 1(b)h(x) =ex/24 Exponentials andlogarithmsExercise 306
5InequalitiesExercise 35Solve the following exponential equations.(a) 3x= 70(b) 3x= 81Exercise 36Use the logarithm laws to show that each ofthe following equations is true for all values ofits variables.(a) ln(12xy3)= lnx+ 3 lnyln 2(b) ln3x212e2x= ln 3 + ln(x2) + ln(x+ 2)2xExercise 37A beefburger is infected with salmonellabacteria, which begin to multiply after2 hours. Tests 6 hours and 8 hours after thetime of the initial infection show that thebeefburger contains about 500 and 5000bacteria per gram, respectively. Assume thatthe number of bacteria in the beefburger canbe modelled using an exponential growthfunctionf, wheref(t) is the number ofbacteria per gram afterthours, for2t12.(a) Find the functionf, stating the constantin the exponent in its rule to foursignificant figures.

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Term
Summer
Professor
NoProfessor
Tags
Topology, Order theory, Complex number

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