MAT 21A Lecture Notes - Lecture 2: Inverse Function, Real Number

• School: UC-Davis
• Department: Mathematics
• Course: MAT 21A
• Professor: Janko Gravner

Document Summary

Mat21a calculus fall 2018 notes & information. Graph of y = x2 + 2x, determine the range. Composite functions is a function that is comprised of 2 or more. If f and g are two functions, the two composite functions that can be formed are: f g(cid:894)(cid:454)(cid:895) = f(cid:894)g(cid:894)(cid:454)(cid:895)(cid:895) f composed with g g f(cid:894)(cid:454)(cid:895) = g(cid:894)f(cid:894)(cid:454)(cid:895)(cid:895) g composed with f and and. Ex) f(x) = x2 + 2x and g(x) = x -1 f(cid:894) (cid:895) = 2 + (cid:1006) f(g(x)) = (g(x))2 + 2(g(x)) Y = f(x) is one to one if and only if each x corresponds to a unqiue y value and each y value only has one x value f(x1(cid:895) f(cid:894)(cid:454)2) when x1 (cid:454)2. If a graph has an imaginary horizontal line that passes through 2 or more points, the function is not one to one.