Question

A contractor is in charge of hiring people for a construction project. The number of days it would take to complete the project with xx full time workers can be found using the function f(x)=\frac{280}{x}.f(x)= x 280 ​ . Assume once workers are assigned to the project, no workers may be added or taken off the project until it is finished. Find and interpret the given function values and determine an appropriate domain for the function.

Answer 1

Answer:

$\text{Domain of x}=[1,\infty), x \in Z^+$

Step-by-step explanation:

Given the function: $f(x)=\dfrac{280}{x}, where:$

f(x) =number of days it would take to complete the project

x =number of full-time workers.

$\text{When x=0, }f(x)=\dfrac{280}{0}= Undetermined\\\text{When x=1, }f(x)=\dfrac{280}{1}= 280 days\\\text{When x=280, }f(x)=\dfrac{280}{280}= 1 day\\\text{When x=560, }f(x)=\dfrac{280}{560}= 0.5 days$

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).

$\text{Domain of x}=[1,\infty), x \in Z^+$