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Let

\[f(x) =
\begin{cases}
|\lfloor{x}\rfloor| &\text{if }x\text{ is rational}, \\
\lceil{x}\rceil^2 &\text{if }x\text{ is irrational}.
\end{cases}
\]

Find $f(\sqrt[3]{-8})+f(-\pi)+f(\sqrt{50})+f\left(\frac{9}{2}\right)$

 Mar 9, 2021
 #1
avatar+201 
+1

\(\begin{align*} f(\sqrt[3]{-8})&=|\lfloor{-2}\rfloor|=2\\ f(-\pi)&=\lceil{-\pi}\rceil^2=-3^2=9\\ f(\sqrt{50})&=\lceil{\sqrt{50}}\rceil^2=8^2=64\\ f\left(\frac{9}{2}\right)&=|\lfloor{\frac{9}{2}}\rfloor|=4\\ 2+9+64+4&=\boxed{79}\\ \end{align*} \)

.
 Mar 9, 2021
edited by jxc516  Mar 9, 2021

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