Question

LetX1={5,10,15,20}andY1={5,10,15,20,25}. Using the formal definition of a func-tion, determine which of the following subsets ofX1×Y1correspond to the functions ofX1→Y1.

Justifyyour answer by providing reasons why each is or is not a function.
a) 1(a)f={(5,20),(10,15),(5,10),(15,5),(20,5)}
b) 1(b)f={(5,25),(10,5),(15,5),(20,10),(5,25)}
c) 1(c)f={(5,5),(10,5),(15,5)}

Answer 1

Option b) is the answer

Explanation:

A function from X₁ to Y₁ is an object f such that every x in X₁ is uniquely associated with an object f(x) = y in Y₁.

Then

1(b)f={(5,25),(10,5),(15,5),(20,10),(5,25)} is the correct answer.

It follows that

f(5) = 25

f(10) = 5

f(15) = 5

f(20) = 10