The domain of g alone is {x | x ≠ 0}, and the domain of f is all reals. So the domain of (f ◦ g) is the domain of g
{x | x ≠ 0}.
(f ◦ g)(x) = 1/x + 3.
The range of g(x) = 1/x is actually the same as its domain {y | y ≠ 0}. Adding three, the range of f ◦ g is all reals except for 3,
{y | y ≠ 3}
The line y = 3 is actually an asymptote (horizontal) to the graph of f ◦ g.
The formula to find the rate of change is y2-y1/x2-x1
6-(-4)/-3-(-1)
=10/-2
=-5
Well if the straight line is equal to 1 then your answer is 2/3 but if the straight line is not equal to 1 you need to know what it is equal to or you could use the equation y = (2/3)x
"x" would be the length of the straight line and "y" would be two-thirds of it
Answer:
The probability is 
Step-by-step explanation:
We can divide the amount of favourable cases by the total amount of cases.
The total amount of cases is the total amount of ways to put 8 rooks on a chessboard. Since a chessboard has 64 squares, this number is the combinatorial number of 64 with 8,
For a favourable case, you need one rook on each column, and for each column the correspondent rook should be in a diferent row than the rest of the rooks. A favourable case can be represented by a bijective function
with A = {1,2,3,4,5,6,7,8}. f(i) = j represents that the rook located in the column i is located in the row j.
Thus, the total of favourable cases is equal to the total amount of bijective functions between a set of 8 elements. This amount is 8!, because we have 8 possibilities for the first column, 7 for the second one, 6 on the third one, and so on.
We can conclude that the probability for 8 rooks not being able to capture themselves is
