Question

The radius r of a circle can be written as a function of the area A with the following equation: What is the domain of this function? Explain why it makes sense in this context.

Answer 1

Answer:

Hence, the domain of the function is:

[0,∞)

Step-by-step explanation:

We know that area of circle is given by the function:

$A=\pi r^2$

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:

$r^2=\dfrac{A}{\pi}\\\\r=\sqrt{\dfrac{A}{\pi}}$

Now as we know that for the square root term to exist:

$\sqrt{\dfrac{A}{\pi}}\geq0$

i.e. $A\geq0$

A=0 represents a point circle since it's area is zero.

Hence, the domain of the function is:

[0,∞)

Answer 2

[0,infinity) because you can not take the radius of a negative mumber.