(Section 1.6: Combining Functions) 1.6.10 Example 7 (“Hidden” Domain Restrictions)Let fx()=1x2±7and gx=x±3. Find f±gxand Domf±g. § SolutionRewriting the rule forfas, say, fu=1u2±7, may clarify the solution. f±gx=fgx=±3•If we had kept the formula =1x2±7, we would informally (and awkwardly) substitute the xin 1x2±7with x±3. Substituting the uin 1u2±7with x±3is less awkward. =1x±32±7=1x±3±7=1x±10x²3; we will explain this
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