Which function has an inverse that is also a function?
1 answer:
Answer:
g(x) = 2x - 3
Step-by-step explanation:
The inverse of a function is the equation where x and y have switched places. If when you solve for y again, the function passes the vertical line test, the inverse if a function.
g(x) = 2x - 3 has inverse x = 2y - 3 which simplifies to y = (x-3)/2. This is a line and is a function y = 1/2 x - 3/2.
k(x) = -9x^2 has the inverse x = -9y^2 which simplifies to . This is a function but only for certain values of x.
f(x) = |x+2| is an absolute value function. All absolute value functions do not have inverses which are functions.
w(x) = -20 does not have an inverse which is a function.
This means A is the solution.
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Answer: The meaning of each term of the Madison’s and Tyler’s expressions is mentioned below.
Step-by-step explanation:
Since, when Madison starts with a population of 1,000 amoebas that triples in size every hour for a number of hours, h.
That is, after 1 hour total number of amoebas = 3×1000 =
After 2 hour, total number of amoebas = 3×3000=
After 3 hour, total number of amoebas = 3×9000=
similarly, after h hours, total number of amoebas,
f(h) =
where, 1000 is the initial population of amoeba 3 is the growth factor of population and f(h) is the population of amoeba after h hours.
Since, when Tyler starts with a population of 1 amoeba that increases 30% in size every hour for a number of hours.
That is, after 1 hour total number of amoebas =
After 2 hour, total number of amoebas =
After 3 hour, total number of amoebas =
Similarly, after h hours, total number of amoebas,
f(h) =
Where, 1 is the initial population of amoeba, 0.3 is the growth rate and 1.3 is the growth factor.
Answer:
The given Expression is sometimes true.
Step-by-step explanation:
from the question,
The given expression by Cary is .
So, solving the expression we get
⇒
Let is an integer.
Whenever,
(a) {
}
The given Expression always gives negative value.
(b) {
}
The given Expression always gives positive value.
Here, we get that the given Expression is not providing the Negative value always, that's why it is not always true and can't be never true.
Hence,
According to Cary's claimantion the given Expression is sometimes true.