Area under the curves, can you make a right choice?

Calculus Level 2

Take a point \(A\) on the graph of \(y=f(x),\) and let \(B\) be a point on the graph of \(y=\sqrt{x}\) such that \(AB\) is parallel to the \(y\)-axis. Call the area bounded by these two curves and the segment \(AB\) as \(R.\)

Now, let \(C\) be a point on the \(y\)-axis such that \(AC\) is parallel to the \(x\)-axis. Call the area bounded by the curve \(y=f(x),\) the \(y\)-axis, and the segment \(AC\) as \(S.\)

Given that the function \(f\) is continuous and the areas \(R\) and \(S\) are equal, which of the following statements is true?

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