Can someone help with this
1 answer:
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Answer:
(- 1, 2)
Step-by-step explanation:
Given a quadratic in standard form y = ax² + bx + c : a ≠ 0
Then the x- coordinate of the vertex is
= -
f(x) = x² + 2x + 3 ← is in standard form
with a = 1 and b = 2, hence
= -
= - 1
Substitute x = - 1 into f(x) for corresponding value of y
f(- 1) = (- 1)² + 2(- 1) + 3 = 1 - 2 + 3 = 2
vertex = (- 1, 2 )
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.