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26_Cal_Solution of Calculus_6e

# 26_Cal_Solution of Calculus_6e - C01S03.017 The domain of...

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C01S03.017: The domain of f ( x ) = x x + 2 is the interval [ 2 , + ), so its graph must be the one shown in Fig. 1.3.38. C01S03.018: The domain of f ( x ) = 2 x x 2 consists of those numbers for which 2 x x 2 0; that is, x (2 x ) 0. This occurs when x and 2 x have the same sign and also when either is zero. If x > 0 and 2 x > 0, then 0 < x < 2. If x < 0 and 2 x < 0, then x < 0 and x > 2, which is impossible. Hence the domain of f is the closed interval [0 , 2]. So the graph of f must be the one shown in Fig. 1.3.36. C01S03.019: The domain of f ( x ) = x 2 2 x consists of those numbers x for which x 2 2 x 0; that is, x ( x 2) 0. This occurs when x and x 2 have the same sign and also when either is zero. If x > 0 and x 2 > 0, then x > 2; if x < 0 and x 2 < 0, then x < 0. So the domain of f is the union of the two intervals ( −∞ , 0] and [2 , + ). So the graph of f must be the one shown in Fig. 1.3.39. C01S03.020: The domain of f ( x ) = 2( x 2 2 x ) 1 / 3 is the set R of all real numbers because every real number has a [unique] cube root. By the analysis in the solution of Problem 19,
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