Answer:
The domain of the function is [tex]D=x|x>0[/tex]
Step-by-step explanation:
Given : The length of a rectangle is 4 units greater than its width, and the area of the rectangle can be expressed by the equation [tex]y=x^2+4x[/tex]
To find : What is a reasonable domain for this function?
Solution :
Domain is defined as the all possible set of values in which function is defined.
We have given the area,
[tex]y=x^2+4x[/tex]
We know, Area will never be negative so the value of x is always positive.
So, [tex]y> 0[/tex]
[tex]x^2+4x>0[/tex]
[tex]x(x+4)> 0[/tex]
i.e. Either [tex]x>0[/tex]
or [tex]x+4> 0[/tex]
[tex]x> -4[/tex] but x>0
So, The value of x is defined from 0 to infinity.
The domain of the function is [tex]D=x|x>0[/tex]
