For any real number $x$, let the function $f(x)$ be the smaller of $2-x^{2}$ and $x$, then the maximum value of $f(x)$ is
1.1 Detailed Explanation: By plotting the graph of the function $f(x)$, we can see that its highest point is $(1,1)$.

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1.1 Detailed Explanation: By plotting the graph of the function $f(x)$,  
we can see that its highest point is $(1,1)$.