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3 years ago

I need some Help please

Mathematics

1 answer:

djverab [1.8K]3 years ago

6 0

Answer:

a) f(2) = 4

b) g(3) = 3

c) g(1/3) = -1

d) f(3) = 1/2

e) g(-2) = 2

f) f(π) = 3

Step-by-step explanation:

We are given:

f={(2,4),(-4,3),(3,1/2),(π,3)} and g={(3,3),(-2,2),(1/3,-1)}

We need to find the following values of f and g

a) f(2)

f(2) means when x=2, we need to find the value of y.

Looking at the given f={(2,4),(-4,3),(3,1/2),(π,3)} , when x =2 then y=4

So, f(2) = 4

b) g(3)

g(3) means when x=3, we need to find the value of y.

Looking at the given g={(3,3),(-2,2),(1/3,-1)}, when x =3 then y=3

So, g(3) = 3

c) g(1/3)

g(1/3) means when x=1/3, we need to find the value of y.

Looking at the given g={(3,3),(-2,2),(1/3,-1)}, when x =1/3 then y=-1

So, g(3) = -1

d) f(3)

f(3) means when x=3, we need to find the value of y.

Looking at the given f={(2,4),(-4,3),(3,1/2),(π,3)} , when x =3 then y=1/2

So, f(3) = 1/2

e) g(-2)

g(-2) means when x=-2, we need to find the value of y.

Looking at the given g={(3,3),(-2,2),(1/3,-1)}, when x =-2 then y=2

So, g(-2) = 2

f) f(π)

f(π) means when x=π, we need to find the value of y.

Looking at the given f={(2,4),(-4,3),(3,1/2),(π,3)} , when x =π then y=3

So, f(π) = 3

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A combination is an unordered arrangement of r distinct objects in a set of n objects. To find the number of permutations, we use the following equation:

n!/((n-r)!r!)

In this case, there could be 0, 1, 2, 3, 4, or all 5 cards discarded. There is only one possible combination each for 0 or 5 cards being discarded (either none of them or all of them). We will be the above equation to find the number of combination s for 1, 2, 3, and 4 discarded cards.

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Notice that discarding 1 or discarding 4 have the same number of combinations, as do discarding 2 or 3. This is being they are inverses of each other. That is, if we discard 2 cards there will be 3 left, or if we discard 3 there will be 2 left.

Now we add together the combinations

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The answer is 32.

-------------------------------

Note: There is also an equation for permutations which is:

n!/(n-r)!

Notice it is very similar to combinations. The only difference is that a permutation is an ORDERED arrangement while a combination is UNORDERED.

We used combinations rather than permutations because the order of the cards does not matter in this case. For example, we could discard the ace of spades followed by the jack of diamonds, or we could discard the jack or diamonds followed by the ace of spades. These two instances are the same combination of cards but a different permutation. We do not care about the order.

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