Question

Determine whether f is a function from the integers to the set of all real numbers.
Enter "Y" for yes and "N" for no.
1. f(n)=±n
2. f(n)=1/(n^2−16)
3. f(n)=√n^2+6
4. f(n)=1/(n^2+9)

Answer 1

1. $f(n)=\pm n$ is not a function, since each number corresponds to two different numbers.
2. $f(n)=\frac{1}{\sqrt{n^2-16}}$ is defined for all numbers, except 4 and therfore is not a function.
3. $f(n)=\sqrt{n^2}+6$ is defined for all numbers. It is a function.
4. $f(n)=\frac{1}{\sqrt{n^2+9}}$ is defined for all numbers. It is a function.