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tester [92]
3 years ago
6

The notation f:S→T denotes that f is a function, also called a map , defined on all of a set S and whose outputs lie in a set T

. A function f:S→T is injective if for all x,y∈S , f(x)=f(y) implies that x=y . Alternatively: a function is injective if we can uniquely recover some input x based on an output f(x) . What functions are injective?
Mathematics
1 answer:
AnnyKZ [126]3 years ago
4 0

Answer:

There are many. Two examples are

f(x) = x, \\f(x) = x^3

Step-by-step explanation:

There are many examples. The simplest is

1 -

f(x) = x

It is trivial that

\text{if \,\,\,\,}  f(x) = f(y) \,\,\,\,\,\text{then} \,\,\,\,\, x=y

2 -

f(x) = x^3

That function is injective as well.

\text{if \,\,\,\,}  x^3 = y^3 \,\,\,\,\,\text{then} \,\,\,\,\, x=y

An example of a function that is NOT injective is

f(x) = x^2

Notice that

f(-2) = (-2)^2 = 2^2 = 4

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Answer:

She served as a queen, for Thutmose ll.

She served as queen alongside her husband, Thutmose II, but after his death, she claimed the role of pharaoh!. She reigned peace, she built temples and monuments, resulting in the flourishing of Egypt!

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2 years ago
Find the sum of the first n terms.
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3 years ago
A water pump fills a swimming pool at a rate of 80
Nat2105 [25]

9514 1404 393

Answer:

  5 hours

Step-by-step explanation:

The volume of the pool is ...

  V = LWH

  V = (10 ft)(8 ft)(5 ft) = 400 ft^3

At the given fill rate, the time it will take is ...

  (400 ft^3)/(80 ft^3/h) = 5 h

It will take 5 hours for the pump to fill the pool.

3 0
3 years ago
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STatiana [176]

Answer:

The missing measurement is 124

Step-by-step explanation:

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Toby put a 13 foot ladder against the side of his house. The distance from the base of the house to the top of the ladder is 12
Serggg [28]

Answer:

<h3>5 feet</h3>

Step-by-step explanation:

The set up will give a right angles triangle with:

length of the ladder as the hypotenuse h = 13 foot

The distance from the base of the house to the top of the ladder is the opposite side (y) = 12 feet

The distance of the base of the ladder from the base of the house wil be the adjacent side (x)

Using the pythagoras theorem to get x:

h² = x²+y²

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x² = 13²-12²

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