MATH114 Lecture Notes - Fall 2018 Lecture 6 - List of Latin phrases (V), Unit circle

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

Document Summary

Math 114 lecture 6 inverses and logarithms continuation. Example: logb(y) = x is equivalent to y = bx. Example: f(t) = y at time t, the amount of 14c is y, the function that gives the time in terms of the 14c-amount is denoted as: So logb undoes the exponential f-1: f-1(y) = t. Example: f(t) = t3 f-1(y) = (cid:1877)(cid:3119) Example: f(x) = x2 f(1) = 1 f(2) = 4 f(-2) = 4. Therefore f-1(4) = is not uniquely defined, can be 2 or -2 function not invertible. Definition: function f is called one-to-one if it never takes the same value more than once. i. e: if x1 x2 f(x1) f(x2) for all x1, x2 in the domain. Example: not inversible f(x) = x2, since f(2) = f(-2) while 2 -2. f(x) = x2. Horizontal blue line intersects graph at more than one place (horizontal line test), therefore not inverse. Solution: graph suggests that the functions is one-to-one.