can anyone help and explain why this is either proportional or not? urgent!! (it needs an explanation too)
1 answer:
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<h2>Answer:</h2>
A function from a set
to a set
is a relation that assigns to each element
in the set
exactly one element
in the set
. The set
is the domain (also called the set of inputs) of the function and the set
contains the range (also called the set of outputs). On the other hand, a function has an inverse function if and only if passes the Horizontal Line Test for Inverse Functions. This test tells us that a function
has an inverse function if and only if there is no any horizontal line that intersects the graph of
at more than one point. So the function is called one-to-one. The graph of
is shown below. As you can see, this function does not pass the Horizontal Line Test, therefore the inverse is not a function. However, let's find
:
and this is not a function because there are elements in the set of inputs that match with two elements in the set of outputs.
4, 5, and 7 are mutually coprime, so you can use the Chinese remainder theorem right away.
We construct a number such that taking it mod 4, 5, and 7 leaves the desired remainders:
- Taken mod 4, the last two terms vanish and we have
so we multiply the first term by 3.
- Taken mod 5, the first and last terms vanish and we have
so we multiply the second term by 2.
- Taken mod 7, the first two terms vanish and we have
so we multiply the last term by 7.
Now,
By the CRT, the system of congruences has a general solution
or all integers ,
, the least (and positive) of which is 27.