Question

Let f:Z→Z be defined by f(m)=2m+1. Determine the range of the function f.

Answer 1

The function f(m)=2m+1 has a range of all odd integers.

Step-by-step explanation:

The function f(x) is defined as f(m)=2m+1, where m is an integer. To determine the range of the function, we need to find all possible values that f(m) can take.

Since f(m) is defined as 2m+1, we know that it will always be an odd integer. The range of the function f is therefore all odd integers.

For example, if we substitute different values of m into the function, we can find corresponding values of f(m). When m=0, f(m)=1. When m=1, f(m)=3. When m=-1, f(m)=-1, and so on. These examples demonstrate that the range of the function f is the set of all odd integers.