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shayla3613
10.03.2021 •
Mathematics
For which pairs of functions is (fog)(x) = x?
1
Х
2
Х
O f(x) = x2 and g(x)=
=
O Rx- and g(x)=
O fx)-*72 and g(x) – 2-3x
O Rx) = 2x-2 and o(x) = 3x+2
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Ответ:
Combinations allow 10,000, permutations allow 5,040.
Step-by-step explanation:
If we allow for repetition, we can have 10^4 possible combinations, if we can start numbers with 0. This is a base 10 system with 4 different objects.
If we don't allow for repetition, we will have 10 possible objects and a subset of 4. Every time we use a digit, we cannot reuse it, so we first have 10 possible digits for the 1st digit.
We have 10*9*8*7 possible combinations if we were to fill in the rest.
0XXX
Since we chose 0, we have 9 other digits remaining (9*8*7 possible permutations)
01XX
8 other digits. (8*7 possible permutations in this system)
018X
7 digits are possible now. (7 possible permutations if we pick 1 more digit)
In conclusion, we would have 10*9*8*7 (10!/6! or 5040) possible permutations in this system. Compared to using combinations where order and reuse is allowed, we have 10^4 possible combinations, or 10000. Combinations win.