For Problems 1-8, if necessary, review Section 1.2. Problems 1-4 refer to the following system of linear inequalities: 4 x + y ≤ 20 3 x + 5 y ≤ 37 x ≥ 0 y ≥ 0 Is the point 2 , 6 in the solution region?
For Problems 1-8, if necessary, review Section 1.2. Problems 1-4 refer to the following system of linear inequalities: 4 x + y ≤ 20 3 x + 5 y ≤ 37 x ≥ 0 y ≥ 0 Is the point 2 , 6 in the solution region?
Solution Summary: The author explains that the point (2,6) lies in the solution region of the provided system of linear inequalities.
7.16. If the probability density of X is given by
g
kx³
for x>0
f(x) = (1+2x)6
0
10-01,
elsewhere
trolls inf
(
2X
density of the random variable Y =
where k is an appropriate constant, find the probability
1+2X
distribution of Y, and thus determine the value of k.
7
Identify the
#2
2. We want to find the inverse of f(x) = (x+3)²
a. On the graph at right, sketch f(x).
(Hint: use what you know about
transformations!) (2 points)
b. What domain should we choose to
get only the part of f (x) that is one-
to-one and non-decreasing? Give
your answer in inequality notation. (2
points)
-
c. Now use algebra to find f¯¹ (x). (2
points)
-4-
3-
2
1
-4
-3
-2
-1
0
1
-1-
-2-
--3-
-4
-N-
2
3
4
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