Mathematics > TEST BANK > Student Solutions Manual to accompany Calculus for Business, Economics, and the Social and Life Scie (All)
1.1 Functions 1. f (x) = 3x + 5, f (0) = 3(0) + 5= 5 f (−1) = 3(−1) + 5= 2 f (2) = 3(2) + 5= 11 3. f (x) = 3x2 + 5x − 2, f (0) = 3(0)2 + 5(0) − 2=−2, f (−2) = 3(−2)2 + 5(−2) −... 2 = 0, f (1) = 3(1)2 + 5(1) − 2 = 6. 5. g(x) = x + 1 x , g(−1)=−1+ 1 −1 =−2, g(1) = 1+ 1 1 = 2, g(2) = 2 + 1 2 = 5 2 . 7. h(t) = t2 + 2t + 4, h(2) = 22 + 2(2) + 4 = 2 √ 3, h(0) = 02 + 2(0) + 4 = 2, h(−4) = (−4)2 + 2(−4) + 4 = 2 √ 3 9. f (t) = (2t − 1) −3/2 = 1 ( √ 2t − 1)3 , f (1) = 1 [ √ 2(1) − 1]3 = 1, f (5) = 1 [ √ 2(5) − 1]3 = 1 [ √ 9]3 = 1 27 , f (13) = 1 [ √ 2(13) − 1]3 = 1 [ √ 25]3 = 1 125 . 11. f (x) = x − |x − 2|, f (1) = 1− |1− 2| = 1− | − 1| = 1− 1= 0, f (2) = 2 − |2 − 2| = 2 − |0| = 2, f (3) = 3− |3− 2| = 3− |1| = 3− 1= 2. 13. h(x) = −2x +4 ifx ≤ 1 x2 +1 ifx >1 h(3) = (3)2 + 1= 10 h(1)=−2(1) + 4 = 2 h(0)=−2(0) + 4 = 4 h(−3)=−2(−3) + 4 = 10 15. g(x) = x 1+ x2 . Since 1+ x2 = 0 for any real number, the domain is the set of all real numbers. 17. f (t) = √ 1− t. Since negative numbers do not have real square roots, the domain is all real numbers such that 1− t ≥ 0, or t ≤ 1. Therefore, the domain is not the set of all real numbers. 19. g(x) = x2 + 5 x + 2 . [Show More]
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