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2 answers:
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Answer:
The inverse of a non-function mapping is not necessarily a function.
For example, the inverse of the non-function mapping is the same as itself (and thus isn't a function, either.)
Step-by-step explanation:
A mapping is a set of pairs of the form . The first entry of each pair is the value of the input. The second entry of the pair would be the value of the output.
A mapping is a function if and only if for each possible input value , at most one of the distinct pairs includes
as the value of first entry.
For example, the mapping is a function. However, the mapping
isn't a function since more than one of the distinct pairs in this mapping include
as the value of the first entry.
The inverse of a mapping is obtained by interchanging the two entries of each of the pairs. For example, the inverse of the mapping is the mapping
.
Consider mapping . This mapping isn't a function since the input value
is the first entry of more than one of the pairs.
Invert as follows:
becomes
becomes
.
becomes
In other words, the inverse of the mapping would be
, which is the same as the original mapping. (Mappings are sets. There is no order between entries within a mapping.)
Thus, is an example of a non-function mapping that is still not a function.
More generally, the inverse of non-trivial ellipses (a class of continuous non-function mappings, including circles) are also non-function mappings.
Answer:
option (b) 0.0228
Step-by-step explanation:
Data provided in the question:
Sample size, n = 100
Sample mean, μ = $20
Standard deviation, s = $5
Confidence interval = between $19 and $21
Now,
Confidence interval = μ ±
thus,
Upper limit of the Confidence interval = μ +
or
$21 = $20 +
or
z = 2
Now,
P(z = 2) = 0.02275 [From standard z vs p value table]
or
P(z = 2) ≈ 0.0228
Hence,
the correct answer is option (b) 0.0228