Answer:
Hence, the domain of the function is:
[0,∞)
Step-by-step explanation:
We know that area of circle is given by the function:
[tex]A=\pi r^2[/tex]
The radius r of a circle can be written as a function of the area A with the following equation:
Now we can represent r in terms of A as:
[tex]r^2=\dfrac{A}{\pi}\\\\r=\sqrt{\dfrac{A}{\pi}}[/tex]
Now as we know that for the square root term to exist:
[tex]\sqrt{\dfrac{A}{\pi}}\geq0[/tex]
i.e. [tex]A\geq0[/tex]
A=0 represents a point circle since it's area is zero.
Hence, the domain of the function is:
[0,∞)
