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If 

\(f(x) = \begin{cases} -\sqrt[3]x & \text{if } x \geq 0,\\ x^2& \text{if } x <0. \end{cases} \)

f(f(f(f(512))))

 Dec 11, 2022
 #1
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\(\begin{align*} f(f(f(f(512)))) &=f(f(f(-8)))\\ &=f(f(64))\\ &=f(-4)\\ &=\boxed{16}. \end{align*}\)

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 Dec 11, 2022

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