Determine whetherfis a function from the set of all bitstrings to the set of integers if

Mathematics

1 answer:

ipn [44]2 years ago

8 0

Answer:

a) Not a function

b) It is a function

c) It is a function

Step-by-step explanation:

a) f(S) is not completly well defined, becuase if the bistring has multiple zeros, you need to pick one and there is not specified method in how you would do so. Another reason for which f is not well defined as a function is that for a bistring with only 1's, f is not defined because there is no zero.

b) This is a function. f(S) returns a concrete and unique integer number for each bistring S. If the bistring has only zeros, the f(S) = 0.

c) This is well defined as a function. It compensates for the failures of the first definition:

- If multiple zeros appears in S, you pick the first one, so there is one possible value for f(S)

-If no zeros appear, f is still well defined because it takes the value 0, as specified in the definition.

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kirill [66]

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what you do from here is isolate all the y terms on one side and all the X terms on the other
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just divided G(y) to both sides and multiply dx to both sides

then integrate both sides
$\int \frac{1}{G(y)} dy = \int F(x) dx

$

once you integrate, you will have a constant. use the initial value condition to solve for the constant, then try to isolate x or y if the question asks for it

In your problem,
$G(y) = \sqrt{1-y^2}

F(x) = 2x$

so all you need to integrate is
$\int \frac{1}{\sqrt{1-y^2}} dy = \int 2x dx$