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shepuryov [24]
4 years ago
12

X = –14.6 and y = 2.5. –x – |y| 

Mathematics
2 answers:
vaieri [72.5K]4 years ago
8 0
Get on algebra calculator (mathpapa) and you should get the answer

zvonat [6]4 years ago
8 0
X = –14.6 and y = 2.5. –x – |y|
replace x and y values into –x – |y|
-(-14.6) - 2.5= 14.6 - 2.5= 12.1hope it helps
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Answer:

Step-by-step explanation:

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

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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.

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Step-by-step explanation:

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