Homework 3 P9Solution1 This is a function because for all in

Homework 3 P9

Solution

1. This is a function because for all integers n , (n^2+3)^(1/2) is a well defined real number.

2. f(n) = 1 /(n^2 9) .

This is not a function with domain Z, since for n = 3 and n = 3 the value of f(n) is not defined by the given rule. In other words, f(3) and f(3) are not specified since division by 0 makes no sense.

3. f(n) = ±n.

This is not a function because the rule is not well-defined. We do not know whether f(n) = n or f(n) = n. For a function, it cannot be both at the same time.

4. f(n) = 1 /(n^2 +8) .

This is a function because for all integers n , 1/(n^2+8) is a well defined real number.