Inverse & Composite

Algebra Level 1

Let \[f(x)= \begin{cases} 1-\sqrt{x} & \text{ if } x\geq 0 \\ \sqrt{1-x} & \text{ if } x<0. \end{cases} \] If \((f^{-1}\circ f^{-1})(a)=100,\) where \(a\) is a constant, what is the value of \(a^2?\)

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