MATH114 Lecture Notes - Lecture 5: Compound Interest, Exponential Function, Logarithm

• School: University of Alberta
• Department: Mathematics
• Course: MATH114
• Professor: Alsaody,Seidon

Document Summary

Math 114 lecture 5 exponential functions (+ logarithms) Last week: trigonometric functions, how to vary functions to get new ones. Example: given y = f(x), construct y = f(x), y = f(x-2), y = 3 + f(x: composition of functions f(x), g(x) ~~~~~~> fog(x), gof(x) Example: f(x) = x2 1, g(x) = (gof)(x) = g(f(x)) = g (x2 1) = (cid:2870) (cid:883) Domain of gof = (- , - 1) u [1, ) Because we can only have positive values inside the square root, any number between - 1 and 1 would generate a negative outcome inside the square root, making it undefined. In general, the domain of gof is all x in domain of f, so that f(x) is in domain of g. These are used to model growth and decay. Definition: exponential functions are functions of the form f(x) = bx (b > 0, base )