Practice Final Exam Answers

 

1.  (a)  [-2, ∞)              (b)  ⅓

 

2.  (a)  g(x) = -2(x – 2)2 + 1                 (b)  1

 

3.  (a)  (f + g)(x) = x2 + 5x -1               (b)  40              (c)  -4              (d)  (f ◦ g)(x) = 9x2 – 1

 

4.  f -1(x) = (x – 2) 5 + 1

 

5.  (Sorry, the graph didn’t show up in the pdf, but the method for (a) would be to look for the y-coordinate when x = -2, and the method for (b) would be to look for the x-coordinate when y = 2.  You can try this with the graph of almost any function.)

 

6.  (a)  x2 + 1 + (8x – 11)/(x2 – 3)                     (b) x3 – x2 – 2x – 1 – 3/(x – 2)

 

7.  just x = -1

 

8.  (a) x = -1 and -4, y = -4                              (b)  V.A.: x = 1,  S.A.: y = x + 6

 

9.  (a)  3           (b)  x + 2          (c)  ½               (d)  0                (e)  -x               (f)  2x

 

10.  ½ ln x – 2 ln y – ln z

 

11.  (a)  2.77                (b)  0                (c)  6, -1

 

12.  (a)  n(t) = 200e0.02789t                     (b)  24.85 days

 

Ex. Cr.  f -1(x) = ln((x + 5)/3) - 2