3. You earned $204 from your job last week. You have two relatives with birthdays coming up and you want to
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:
The population will be 896 turtles 6 years later ⇒ B
Step-by-step explanation:
The exponential increasing formula is y = a, where
- y is the new value
- a is the initial value
- r is the rate of increase in decimal
- x is the time in years
∵ There are 300 turtles
∴ a = 300
∵ The population of the turtles exponentially increases 20% each year
∴ r = 20%
→ Divide it by 100 to change it to decimal
∵ 20% = 20 ÷ 100 = 0.2
∴ r = 0.2
∵ The time is 6 years
∴ x = 6
→ Substitute these values in the exponential formula above
∵ y = 300
∴ y = 300
∴ y = 895.7952
→ Round it to the nearest whole number
∴ y = 896
∴ The population will be 896 turtles 6 years later