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Student Solutions Manual to accompany Calculus for Business, Economics, and the Social and Life Sciences Tenth Edition, Brief Laurence D. Hoffman Smith Barney Gerald L. Bradley Claremon McKenna College Prepared by

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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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