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3.3 The logarithm as an inverse function

3.To nd the inverse of y= 5 + ex we swap variables, subtract 5 from both sides and then take the natural log to get ln(x 5) = y:So f 1(x) = ln(x 5) : 4.To nd the inverse of f(x) = log 2 (x+ 2) + 2 we write y= log 2 (x+ 2) + 2; change variables (to indicate that we are swapping inputs and outputs)

Optimization Techniques - Sam Houston State University

4 WEB CHAPTER A Optimization Techniques ( ) relationships. The technique of Lagrangian multiplierscan be used to find the opti- mal solution to many of these problems. Often, however, the constraints in an economic decision-making problem take the

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