Find the value of h(45) for the function below.
h(x) = {(90 – 5)
what’s the value
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Ответ:
Inverse Functions
One-to-one
Suppose f : A ⇥ B is a function. We call f one-to-one if every distinct
pair of objects in A is assigned to a distinct pair of objects in B. In other
words, each object of the target has at most one object from the domain
assigned to it.
There is a way of phrasing the previous definition in a more mathematical
language: f is one-to-one if whenever we have two objects a, c ⇤ A with
a ⌅= c, we are guaranteed that f(a) ⌅= f(c).
Example. f : R ⇥ R where f(x) = x2 is not one-to-one because 3 ⌅= 3
and yet f(3) = f(3) since f(3) and f(3) both equal 9.
Horizontal line test
If a horizontal line intersects the graph of f(x) in more than one point,
then f(x) is not one-to-one.
The reason f(x) would not be one-to-one is that the graph would contain
two points that have the same second coordinate – for example, (2, 3) and
(4, 3). That would mean that f(2) and f(4) both equal 3, and one-to-one
functions can’t assign two dierent objects in the domain to the same object
of the target.
If every horizontal line in R2 intersects the graph of a function at most
once, then the function is one-to-one.
Examples. Below is the graph of f : R ⇥ R where f(x) = x2. There is a
horizontal line that intersects this graph in more than one point, so f is not
one-to-one.
66
Inverse Functions
One-to-one
Suppose f : A —* B is a function. We call f one-to-one if every distinct
pair of objects in A is assigned to a distinct pair of objects in B. In other
words, each object of the target has at most one object from the domain
assigned to it.
There is a way of phrasing the previous definition in a more mathematical
language: f is one-to-one if whenever we have two objects a, c e A with
a ~ c, we are guaranteed that f(a) $ f(c).
Example. f : IR —* JR where f(x) = x2 is not one-to-one because 3 ~ —3
and yet f(3) = f(—3) since f(3) and f(—3) both equal 9.
Horizontal line test
If a horizontal line intersects the graph of f(.x) in more than one point,
then f(z) is not one-to-one.
The reason f(x) would not be one-to-one is that the graph would contain
two points that have the same second coordinate — for example, (2,3) and
(4,3). That would mean that f(2) and f(4) both equal 3, and one-to-one
functions can’t assign two different objects in the domain to the same object
of the target.
If every horizontal line in JR2 intersects the graph of a function at most
once, then the function is one-to-one.
Examples. Below is the graph of f : JR —, R where f(z) = z2. There is a
horizontal line that intersects this graph in more than one point, so f is not
Explanation:
Ответ:
Note: The equation I'm giving an answer to looks like this h(x)=1/9(90-x) the answer is 5
Explanation:
Because h(x) is the same as a Y in the formula y=mx+b so 5 = 1/9(90-x) which is the value of 45.
Ответ:
I agree because the rule of the Mongols in central Asia concur with the peak of Silk Road trade between 600 and 1450 C.E. The postclassical world falls between the years 200-600 and 1200-1500 and the silk road was at its peak during thisera. Although the silk road did see some decline after the classical empires of China, India and Rome had all crashed, it was still existent and grew to be bigger.