Answer:
[tex]\text{Domain of x}=[1,\infty), x \in Z^+[/tex]
Step-by-step explanation:
Given the function: [tex]f(x)=\dfrac{280}{x},$ where:[/tex]
f(x) =number of days it would take to complete the project
x =number of full-time workers.
[tex]\text{When x=0, }f(x)=\dfrac{280}{0}=$Undetermined\\\text{When x=1, }f(x)=\dfrac{280}{1}=$280 days\\\text{When x=280, }f(x)=\dfrac{280}{280}=$1 day\\\text{When x=560, }f(x)=\dfrac{280}{560}=$0.5 days[/tex]
The domain of a function is the complete set of possible values of the independent variable.
In this case, the independent variable is x, the number of full-time workers. We have shown that x cannot be zero as there must be at least a worker on ground.
Therefore, an appropriate domain of the function f(x) is the set of positive integers (from 1 to infinity).
[tex]\text{Domain of x}=[1,\infty), x \in Z^+[/tex]
