ExplanationIf \(x\) is odd, \(\alpha (x)\) equals the least integer greater than x (e.g., if x = 3, then the “least integer greater than 3” is equal to 4)
If \(x\) is even, \(\alpha (x)\) equals the greatest integer less than x (e.g., if x = 6, the “greatest integer less than x” is equal to 5.
Since –2 is even, \(\alpha (-2)\) the greatest integer less than –2, or –3.
Since \(5\) is odd, \(\alpha(5)=\) the least integer greater than 5, or 6.
Thus, \(\alpha(-2)-\alpha(5) = -3 - 6 = -9\).
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