Clicker Question 1 On what restricted domain is f (x) = (x – 2) 2 a one-to-one function? A. x  0 B. x  2 C. x  -2 D. x  4 E. all reals (no need to restrict)

Clicker Question 2 Find a formula (y as a function of x ) for the inverse of y = tan(3x + 1). A. y = tan((x – 1)/3) B. y = arctan((x – 1)/3) C. y = (tan(x ) – 1)/3 D. y = (arctan(x ) – 1)/3 E. y = arctan(3x + 1)

Logarithmic Functions (10/3/11) Logarithmic functions (“log” functions) are the inverses of exponential functions. That is, an exponential function has as input an exponent on a fixed base, whereas a log function has the exponent on a fixed base as output !! For example, the log function log 10 (x) has as output the exponent on 10 to give you x. Hence, for example, log 10 (1000) = 3.

Clicker Question 3 What is log 2 (64)? A B. 4 C. 6 D. 8 E. I’m allergic to log functions

Domain, Range and Notation Since the range of the exponential function a x is all positive numbers, that will be the domain of the corresponding log function. What about range of log functions? Notation: log a (x ) has base a (>0). log (x ) normally means the base is 10. ln (x ) has base e (“Natural log”)

Properties of Log Functions Since the output of logs are exponents, all log functions: Turn products into sums, i.e., log(A B) = log(A) + log(B) Turn quotients into differences, i.e., log(A / B) = log(A) – log(B) Turn exponents into coefficients, i.e., log(A p ) = p log(A)

Using Logs to Solve Equations Because logs are the inverses of exponential functions, they are used to solve any equation in which the unknown is an exponent. Simply take the log (any base you wish) of both sides and use the property of logs that they turn exponents into coefficients. Example: If 5 x = 15, then ln(5 x ) = ln(15), so x ln(5) = ln(15), so x = ln(15) / ln(5) = 1.683

Assignment for Wednesday Read pages 62 (bottom) - 66 of Section 1.6 In that section, please do Exercises 23, 25, 33, 35, 37, 39, 51, 53, 55. Get to work on Hand-in #2 (due Thursday at 4:45)