Write a rule expressing the area of a circle as a function of its radius. What is the domain of the object?
a(r)=πr²
This is a function. The right hand side is the rule. r is the independent variable. The domain of r (i.e. the values it can assume) is ℝ+, meaning all positive real values, since we do not have a negative radius.
Does this have an inverse?
The formula to calculate the area of a circle is given by:
A = πr^2
where A represents the area of the circle and r represents its radius. This formula relates the area of the circle to the square of its radius.
In terms of the domain of the object, the radius of a circle can be considered as a positive real number. Thus, the domain of the object, in this case, is all positive real numbers. This means that any positive real number can be used as the radius to find the corresponding area of a circle using the formula mentioned above.