2 2 1 y x x 5 y x 2 2 1 5 x x x 2 2 1 5 x x x 2 3 4 x

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Mathematical Applications for the Management, Life, and Social Sciences
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Chapter 5 / Exercise 7
Mathematical Applications for the Management, Life, and Social Sciences
Harshbarger
Expert Verified
221yxx5yx2215xxx22150xxx 2340xx(1)(4)0xx1x or 4xSubstitute 1x and 4xinto 5yx4yand 9yPoints of intersection are (-1, 4) and (4, 9).
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Mathematical Applications for the Management, Life, and Social Sciences
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Chapter 5 / Exercise 7
Mathematical Applications for the Management, Life, and Social Sciences
Harshbarger
Expert Verified
4 (ii)242yxxand 21yxSolve both equations for yand equate the y-values. 242yxx21yx 24221xxx 242210xxx 2230xx(1)(3)0xx1x or 3xSubstitute 1x and 3xinto 21yx 3yand 5y Points of intersection are (-1, 3) and (3, -5). 2.Finding domain and range of the function and composite function.a.Find the domain and range of the function (i)( )23xf xx(ii) ( )31f xxSet 230x32xSet 310x 13xDomain is 32{ /}xxor 3322(,)( ,)Domain is 13{ /}xxor 13[ ,)Range is (,) Range is [0,). b.Given ( )f xxand 2( )21g xx, find ()( )fgxoand ()( )gfxo.()( )( ( ))fgxf g xo()( )(( ))gfxg f xo22(21)21fxx= ()gx22()121xx2()( )21fgxxo()( )21gfxxo3.Exponential and Logarithmic Functions.a.Use the properties of Logarithm to expand the following expression and simplify. (i)2323ln()lnlnlnx yexye(ii) 331log ()log 1logbbbbb2ln3ln1xylog 13logbbb0323ln()2ln3ln1x yexy31log ()3bb 
5 b.Solve the following exponential and logarithmic equations for x.(i)(5 3 )2xe(ii) ln(3)ln(21)ln3xx(5 3 )ln[]ln2xeln[(3)(21)]ln3xx(53 )lnln2xeln[(3)(21)]ln3xxee(53 )ln2x(3)(21)3xx3ln25x22733xx13(ln25)x 2270xx13(5ln2)x(27)0xx0xand 72xSolution is 13(5ln2)xSolutions are0xand 72x 4.Evaluating Inverse Trigonometric Functions. a.132sin()b. 14tan(cos( ))xLet 132sin()y, 22yLet 14cos( )xy, 0y132sinsin(sin())y14coscos(cos( ))xy32siny4cosxy3y216tanxyx132sin()321416tan(cos( ))xxx

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