C01S03.017:The domain off(x) =x√x+ 2 is the interval [−2,+∞), so its graph must be the oneshown in Fig. 1.3.38.C01S03.018:The domain off(x) =√2x−x2consists of those numbers for which 2x−x20; that is,x(2−x)0. This occurs whenxand 2−xhave the same sign and also when either is zero. Ifx >0 and2−x >0, then 0< x <2. Ifx <0 and 2−x <0, thenx <0 andx >2, which is impossible. Hence thedomain offis the closed interval [0,2]. So the graph offmust be the one shown in Fig. 1.3.36.C01S03.019:The domain off(x) =√x2−2xconsists of those numbersxfor whichx2−2x0; thatis,x(x−2)0. This occurs whenxandx−2 have the same sign and also when either is zero. Ifx >0andx−2>0, thenx >2; ifx <0 andx−2<0, thenx <0. So the domain offis the union of the twointervals (−∞,0] and [2,+∞). So the graph offmust be the one shown in Fig. 1.3.39.C01S03.020:The domain off(x) = 2(x2−2x)1/3is the setRof all real numbers because every realnumber has a [unique] cube root. By the analysis in the solution of Problem 19,
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