MTH 230 Study Guide - Midterm Guide: Identity Function, Floor And Ceiling Functions, Binary Operation

• School: University of Miami
• Department: Mathematics
• Course: MTH 230
• Professor: Ramakrishnan

Document Summary

Test 4 abstract: give example of equivalent functions. If x is the domain and it has m elements & y is the co-domain and it has n elements, the: explain how to find how many functions are possible, give notation. A function f with domain (set of inputs) x and co-domain (set of outputs) y ((cid:1858): (cid:1850) (cid:1851)) associates with each element (cid:1876) (cid:1850) a unique element (cid:1877) (cid:1851). The y is called the value of the function f at x & is denoted by (cid:1858)(cid:4666)(cid:1876)(cid:4667). number of functions possible is (cid:1866)(cid:3040). (cid:1851)(cid:3051) is the notation for the number of functions from x to y. We say that (cid:1858)=(cid:1859) if (cid:1850)=(cid:1847),(cid:1851)=(cid:1848),& (cid:1858)(cid:4666)(cid:1876)(cid:4667)=(cid:1859)(cid:4666)(cid:1876)(cid:4667) (cid:1876) (cid:1850). Let & (cid:1859): be defined by (cid:1859)(cid:4666)(cid:1876)(cid:4667)= (cid:4672)(cid:1876) (cid:2869)(cid:3051)(cid:4673)(cid:2870)+(cid:886). They are equivalent functions since the domains & codomains are the same & (cid:1859)(cid:4666)(cid:1876)(cid:4667)= (cid:4672)(cid:1876) (cid:2869)(cid:3051)(cid:4673)(cid:2870)+(cid:886)= (cid:1876)(cid:2870) (cid:884)+ (cid:2869)(cid:3051)2+(cid:886)= (cid:1876)(cid:2870)+(cid:884)+ (cid:2869)(cid:3051)2= (cid:4672)(cid:1876)+(cid:2869)(cid:3051)(cid:4673)(cid:2870)