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{231}{x}.f(x)=
x
231
​
. 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.

f(-−3)=
, meaning with
full time workers, the project would be complete in
days. This interpretation
in the context of the problem.
f(7)=
, meaning with
full time workers, the project would be complete in
days. This interpretation
in the context of the problem.
f(5.5)=
, meaning with
full time workers, the project would be complete in
days. This interpretation
in the context of the problem.
Based on the observations above, it is clear that an appropriate domain for the function is
.
need answers asap please

Answer 1

The domain of the function is x is a set of positive integers.  

How to get the domain?

We are given the function; f(x) = 126/x. f(x) is the number of days it would take to complete a project and x is the number of workers

The domain is defined as the set of all possible input values for which the function is defined.

Let's try x = 0 workers.

f(x) = 126/0 ; this is undefined and so x cannot be zero.

Let's try x = 1 worker

f(x) = 126/1 = 126 days

Let's try x = 10 workers

f(x) = 126/10 = 12.6 days

Let's try x = 100 workers

f(x) = 126/100 = 1.26 days

We see that every positive integer is a possible value of x that can make the function defined. Thus, the domain of the function is x is a set of all positive integers.

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