Problem

\(A(r)~=~\pi~r^2\) gives circle area in square meters from radius \(r~\ge~0\) meters. Describe the forward and inverse mappings with units, write \(A^{-1}(s)\), and explain how \(r~\ge~0\) ensures uniqueness.

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Forward: A maps nonnegative radius r, in meters, to area s, in square meters. Inverse: A⁻¹ maps radius r to area, in square meters. Formula: A⁻¹(r)=πr², using r≥0 for uniqueness.

Forward: A maps nonnegative radius r, in meters, to area s, in square meters. Inverse: A⁻¹ maps area s to the unique nonnegative radius, in meters. Formula: A⁻¹(s)=√(s/π), using r≥0 for uniqueness.

Forward: A maps nonnegative radius r, in meters, to area s, in square meters. Inverse: A⁻¹ maps area s to two signed radii, in meters. Formula: A⁻¹(s)=±√(s/π), despite the domain r≥0.

Forward: A maps nonnegative radius r, in square meters, to area s, in square meters. Inverse: A⁻¹ maps area s to a radius, in square meters. Formula: A⁻¹(s)=√(s/π), using r≥0 for uniqueness.

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\(A(r)~=~\pi~r^2\) gives circle area in square meters from radius \(r~\ge~0\) meters. Describe the forward and inverse mappings with units, write \(A^{-1}(s)\), and explain how \(r~\ge~0\) ensures uniqueness.

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