MAT 1300 Lecture Notes - Lecture 3: Inverse Function

• School: University of Ottawa
• Department: Mathematics
• Course: MAT 1300
• Professor: Dongyang Kuang

Document Summary

Inverse functions are continued from the lecture 3 note. Definition: g" is an inverse function of f" if f(g(x))=x and g(f(x))=x. To find the inverse, use the following procedure: take the function and switch x and y, solve this equation for y. [x=y-1/2y+1](2y+1) x(2y+1)= y-1 *side: distribute the x into the bracket (2y+1) 2xy+x= y-1 now try to get all of the y"s on the left side. Therefore the inverse, f-1(x), of y=x-1/2x+1 is y=-x-1/2x-1. Definition: if f(x) gets arbitrarily close to l, a number, as x approaches c from either side, we write lim f(x)= l. The limit of f(x) as x approaches c is l". *note: consider numbers to the left of 2 and to the right of 2 x. The limit equals 7 because as shown in the chart above, 7 is the. X 2 number between the left side and right side of 2. *note: 3 is not in the domain of the function.