PLSSS HELPPPPPP I WILL MARK BRAINLIEST!!!!!!!<br><br> THIS IS A solve multistep inequalities PROBLEM

Daniel [21]

Answer:

Step-by-step explanation:

As the statement is ‘‘if and only if’’ we need to prove two implications

$f : X \rightarrow Y$ is surjective implies there exists a function $h : Y \rightarrow X$ such that $f\circ h = 1_Y$ .
If there exists a function $h : Y \rightarrow X$ such that $f\circ h = 1_Y$ , then $f : X \rightarrow Y$ is surjective

Let us start by the first implication.

Our hypothesis is that the function $f : X \rightarrow Y$ is surjective. From this we know that for every $y\in Y$ there exist, at least, one $x\in X$ such that $y=f(x)$ .

Now, define the sets $X_y = \{x\in X: y=f(x)\}$ . Notice that the set $X_y$ is the pre-image of the element $y$ . Also, from the fact that $f$ is a function we deduce that $X_{y_1}\cap X_{y_2}=\emptyset$ , and because $f$ the sets $X_y$ are no empty.

From each set $X_y$ choose only one element $x_y$ , and notice that $f(x_y)=y$ .

So, we can define the function $h:Y\rightarrow X$ as $h(y)=x_y$ . It is no difficult to conclude that $f\circ h(y) = f(x_y)=y$ . With this we have that $f\circ h=1_Y$ , and the prove is complete.

Now, let us prove the second implication.

We have that there exists a function $h:Y\rightarrow X$ such that $f\circ h=1_Y$ .

Take an element $y\in Y$ , then $f\circ h(y)=y$ . Now, write $x=h(y)$ and notice that $x\in X$ . Also, with this we have that $f(x)=y$ .

So, for every element $y\in Y$ we have found that an element $x\in X$ (recall that $x=h(y)$ ) such that $y=f(x)$ , which is equivalent to the fact that $f$ is surjective. Therefore, the prove is complete.

3 0

3 years ago

8. Chloe received $20.00 for her birthday. She

Leni [432]

Answer: $9.23

because you multiply 3.59 by 3 to get $10.77 which was spent then you subtract $10.77 from $20.

4 0

3 years ago

The difference in age between Brita and her daughter Eva is 30 years. The sum or their ages 118. How old is Eva?

Alona [7]

Answer:

Eva's age is 44 years

Step-by-step explanation:

Let

x ----> Brita's age

y ----> Eva's age

we know that

The sum or their ages 118

so

$x+y=118$ ----> equation A

The difference in age between Brita and her daughter Eva is 30 years

so

$x-y=30$ ----> equation B

Solve the system by elimination

Adds equation A and equation B

$x+y=118\\x-y=30\\---------\\x+x=118+30\\2x=148\\x=74$

<em>Find the value of y</em>

substitute the value of x in any equation

$74+y=118\\y=118-74\\y=44$

therefore

Eva's age is 44 years

3 0

3 years ago

Please help me with this, and an explanation if possible.

goldfiish [28.3K]

Answer:

D

Step-by-step explanation:

To find the inverse. Switch the x and y and re solve for y

multiply both sides by 6 and subtract both sides by 54

4 0

3 years ago

The ratio of pencils to erasers is 1:2. There are 24 pencils and erasers in all. How many pencils and erasers are there?

Semenov [28]

There are 8 pencils and 16 erasers.

Step-by-step explanation:

Given,

Ratio of pencils to eraser = 1:2

Total number of pencils and erasers = 24

Let,

x be the original number.

Therefore,

Number of pencils = x

Number of erasers = 2x

Thus,

x+2x = 24

$3x=24$

Dividing both sides by 3

$\frac{3x}{3}=\frac{24}{3}\\x=8$

Number of pencils = 8

Number of erasers = 2(8) = 16

There are 8 pencils and 16 erasers.

Keywords: ratio, division

Learn more about ratio at:

#LearnwithBrainly

3 0

4 years ago

PLSSS HELPPPPPP I WILL MARK BRAINLIEST!!!!!!! THIS IS A solve multistep inequalities PROBLEM