solution:
We are going to use this property: P(A U B) = P(A) + P(B) – P(AB)
First we treat (A U B) as one event as follows:
P( (A U B) U C) = P( A U B ) + P(C) – P((A U B)C)
= P( A U B ) + P(C) – P(AC U BC)
= P(A) + P(B) – P(AB) + P(C) – P(C) – P(AC U BC )
=P(A) + P(B) – P(AB) + P(C) –P(AC) – P(BC) + P(ABC)
= P(A) + P(B) + P(C) – P(AB) – P(AC) – (BC) + P(ABC)
Slope is the change in y over the change in x:
Slope = (y2 - y1) / (x2-x1)
Replace the letters in the equation with the given information:
1/2 = (1 - -1) / (15 -r)
Cross multiply:
1 * (15-r) = 2 * (1- -1)
Simplify:
15 -r = 4
Subtract 15 from each side:
-r = -11
Because r is negative, you need to multiply both sides by -1 to make r positive:
r = 11
The one-to-one functions given as sets of points and their possible inverse functions are given as
h = { (1,1), (2,2), (3,3), (4,4), (5,5), (6,6)}
g = { (1,3), (2,6), (3,9), (4,12), (5,15), (6,18)}
f = { (1,2), (2,3), (3,4), (4,5), (5,6), (6,7)}
i = { (1,1), (2,3), (3,5), (4,7), (5,9), (6,11)}
h⁻¹ = { (1,1), (2,2), (3,3), (4,4), (5,5), (6,6)}
i⁻¹ = { (1,1), (3,2), (5,3), (7,4), (9,5), (11,6)}
g⁻¹ = {(3,1), (6,2), (9,3), (12,4), (15,5), (18,6)}
f⁻¹ = {(2,1), (3,2), (4,3), (5,4), (6,5), (7,6)}
The inverse function of a given function should have the coordinates reversed.
Therefore the matches between the given functions and their inverse functions are given in the table below.
function Inverse function
----------- ------------------------
h h⁻¹
g g⁻¹
f f⁻¹
i i⁻¹
Answer:
The given functions and their corresponding inverses are correct.
