Stitz-Zeager_College_Algebra_e-book

# For example h3 is not dened because t 3 doesnt satisfy

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Unformatted text preview: h. Hence, the domain is (−∞, ∞). 4. To ﬁnd the domain of r, we notice that we have two potentially hazardous issues: not only do we have a denominator, we have a square root in that denominator. To satisfy the square root, we set the radicand x + 3 ≥ 0 so x ≥ −3. Setting the denominator equal to zero gives 6− √ x+3 6 62 36 33 = = = = = 0 √ x+3 √ x+3 x+3 x 2 Since we squared both sides in the course of solving this equation, we need to check our √ √ answer. Sure enough, when x = 33, 6 − x + 3 = 6 − 36 = 0, and so x = 33 will cause problems in the denominator. At last we can ﬁnd the domain of r: we need x ≥ −3, but x = 33. Our ﬁnal answer is [−3, 33) ∪ (33, ∞). 2 x 5. It’s tempting to simplify I (x) = 3x = 3x, and, since there are no longer any denominators, claim that there are no longer any restrictions. However, in simplifying I (x), we are assuming 0 x = 0, since 0 is undeﬁned.4 Proceeding as before, we ﬁnd the domain of I to be all real numbers except 0: (−∞, 0) ∪ (0, ∞). It is worth reiter...
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## This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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