Economics 3364A/B Lecture 1: Calc Quiz 1-2

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Find a formula for the inverse of f (x), as well as the domain of f 1(x). Solving this equation for x as follows: y(ex + 1) = ex 1 = yex + y = ex 1 = yex ex = 1 y. = ex(y 1) = (1 + y) = ex = 1 x , that is f 1 = ln 1+x. 1 x > 0 gives the domail of f 1 which is: 1 < x < 1. Interchanging the positions of x and y gives: y = ln 1+x. Solving inequality 1+x: simplify log5 10 + log5 40 4 log5 2. Solution: using the properties for log functions, one obtains: log5 10 + log5 40 4 log5 2 = log5(10 40) log5 24 = log5. 24 = log5 52 = 2 log5 5 = 2: solve the equation ln(2x 1) ln x = 0 for x.

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