Unformatted text preview: x âˆš x âˆ’ 2 = p x 2 âˆ’ 2 x, and Âµ f g Â¶ ( x ) = âˆš x âˆš x âˆ’ 2 = r x x âˆ’ 2 . C01S03.004: The domain of f is the interval [ âˆ’ 1 , + âˆž ) and the domain of g is the interval ( âˆ’âˆž , 5]. Hence the domain of f + g and f Â· g is the closed interval [ âˆ’ 1 , 5], but because g (5) = 0, the domain of f/g is the halfopen interval [ âˆ’ 1 , 5). Their formulas are ( f + g )( x ) = âˆš x + 1 + âˆš 5 âˆ’ x, ( f Â· g )( x ) = âˆš x + 1 âˆš 5 âˆ’ x = p 5 + 4 x âˆ’ x 2 , and Âµ f g Â¶ ( x ) = âˆš x + 1 âˆš 5 âˆ’ x = r x + 1 5 âˆ’ x . C01S03.005: The domain of f is the set R of all real numbers; the domain of g is the open interval ( âˆ’ 2 , 2). Hence the domain of f + g and f Â· g is the open interval ( âˆ’ 2 , 2); because g ( x ) is never zero, the domain of f/g is the same. Their formulas are 1...
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This note was uploaded on 09/14/2011 for the course MATH 101 taught by Professor Cheng during the Spring '11 term at Ecole HÃ´teliÃ¨re de Lausanne.
 Spring '11
 CHENG
 Calculus, Real Numbers

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