Precalc0105to0107-page22

Precalc0105to0107-page22 - (Section 1.6 Combining Functions...

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(Section 1.6: Combining Functions) 1.6.10 Example 7 (“Hidden” Domain Restrictions) Let fx () = 1 x 2 ± 7 and gx = x ± 3 . Find f ± g x and Dom f ± g . § Solution Rewriting the rule for f as, say, fu = 1 u 2 ± 7 , may clarify the solution. f ± g x = fgx = ± 3 If we had kept the formula = 1 x 2 ± 7 , we would informally (and awkwardly) substitute the x in 1 x 2 ± 7 with x ± 3 . Substituting the u in 1 u 2 ± 7 with x ± 3 is less awkward. = 1 x ± 3 2 ± 7 = 1 x ± 3 ± 7 = 1 x ± 10 x ² 3; we will explain this
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