Answer:
The area function is
.
The domain and range of A is
and
.
Step-by-step explanation:
The given length of fencing is
.
Let the length and width of each pen be
and
respectively as shown in the figure.
As there are 3 pens, so, the total area,

From the figure the total length of fencing is
.
Here, for a significant area for the animals,
as well as
as
and
are the sides of ben.
From the given value:


Now, from equation (i)


This is the required area function in the terms of variable
.
For the domain of area function, from equation (ii)

[as y>0]
So, the domain of area function is
.
For the range of area function:
As
or
, then
[from equation (i)]

Now, differentiate the area function with respect to
.

Equate
to zero to get the extremum point.



Check this point by double differentiation

As,
, so, point
is corresponding to maxima.
Put this value back to equation (iii) to get the maximum value of area function. We have


Hence, the range of area function is
.