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高中数学必修 第一册(648题)


已知 \( f\left(x\right)=\left\{\begin{array}{c}x+2, x\le -1\\ {x}^{2},-1<x<2\\ 2x, x\ge 2\end{array}\right.\),求 \( f(-\pi )\) 及 \( f\left(f\right(\frac{3}{2}\left)\right)\) 的值.



知识点:第三章 函数的概念与性质


参考答案:∵\(-\pi <-1\),\(∴f(-π)=-π+2\).

∵\( -1<\frac{3}{2}<2\),\(\therefore f\left ( {\frac {3} {2}} \right )=\left ( {\frac {3} {2}} \right )^{2}=\frac {9} {4}>2\).

\(\therefore f\left ( {f\left ( {\frac {3} {2}} \right )} \right )=f\left ( {\frac {9} {4}} \right )=2\times \frac {9} {4}=\frac {9} {2}\).

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