14．已知函数 $f(x)=\left\{\begin{array}{c}-x^{2}+2, x \leq 1, \\ x+\frac{1}{x}-1, x>1,\end{array}\right.$ 则 $f\left(f\left(\frac{1}{2}\right)\right)=$ $\_\_\_\_$ ；若当 $x \in[a, b]$ 时， $1 \leq f(x) \leq 3$ ，则 $b-a$ 的最大值是 $\_\_\_\_$ ．
对勾函数 · 历年高考数学真题与解析
本页汇总 高考真题检索 的「对勾函数」高考数学真题共 2 道，覆盖 2008–2022 年，最常出题型为 填空题；含完整答案与解析。
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3．若函数 $y=f(x)$ 的值域是 $\left[\frac{1}{2}, 3\right]$ ，则函数 $F(x)=f(x)+\frac{1}{f(x)}$ 的值域是
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