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Algebra Difficulty 4.0 AMC 10/12 Find the answer China

The range of f(x)=x5243xf(x) = \sqrt{x-5} - \sqrt{24-3x} is ______.

A number or a short expression. Spacing and $ signs are ignored.

Solution

It is easy to see that f(x)f(x) is increasing on its domain [5,8][5, 8]. Therefore, its range is [3,3][-3, \sqrt{3}].

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