Chapter 1.1, Problem 32PPSE

Solution

To write a rule that gives an even number for each and every input.

The rule $f\left(n\right)=2n$ where $n$ is an integer, is an example of a rule giving an even output for each input.

Concept used:

Even number:

An even number is an integer that is divisible by $2$ .

Calculation:

Consider the rule $f\left(n\right)=2n$ where $n$ is an integer.

Clearly, $\frac{f\left(n\right)}{2}=n$ .

That is, $f\left(n\right)$ is divisible by $2$ for each $n$ .

Thus, the rule $f\left(n\right)=2n$ where $n$ is an integer, is an example of a rule giving an even output for each input.

Conclusion:

The rule $f\left(n\right)=2n$ where $n$ is an integer, is an example of a rule giving an even output for each input.