Solve the equation without using the Distributive Property.

Give an example of a function f : N → N that is surjective but not injective. You must explain why your example is surjective an

Helen [10]

Answer:

Consider f: N → N defined by f(0)=0 and f(n)=n-1 for all n>0.

Step-by-step explanation:

First we will prove that f is surjective. Let y∈N be any natural number. Define x as the number x=y+1. Then x∈N, and f(x)=x-1=(y+1)-1=y. We conclude that f is surjective.

However, f is not injective. Take x1=0 and x2=1. Then x1≠x2 but f(x1)=0 and f(x2)=x2-1=1-1=0. We have shown that there are two natural numbers x1,x2 such that x1≠x2 but f(x1)=f(x2), that is, f is not injective.

Note:

If 0∉N in your definition of natural numbers, the same reasoning works with the function f: N → N defined by f(1)=1 and f(n)=n-1 for all n>1. The only difference is that you consider x1=1, x2=2 for the injectivity.

7 0

3 years ago

2,12,72,432 what is the formula?

egoroff_w [7]

Answer: The formula is x6

Step-by-step explanation:

4 0

3 years ago

If the product of a number and -4 is subtracted from the number, the result is 3 more than the number. Find the number

lesya [120]

Answer: The number is 0.75 or 3/4

Step-by-step explanation:

let x = the number.

Now set up an equation: The product of a number (x) and -4 = -4x. So -4x is subtracted from the number - x. x-(-4x)

Then, that equals 3 more than the number (x) = x+3

So the equation is x-(-4x)=x+3.

Then, solve the equation!

x-(-4x)=x+3

x+4x=x+3 (Distribute the negative to the parentheses)

5x=x+3 (Combine like terms)

4x=3 (Get the Xs on one side by subtracting x from both sides)

x=0.75 or 3/4 (divide by the coefficiant, 4, on both sides)

3 0

3 years ago

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Un capital de 4000 lei este plasat în regim de dobândă simplă pe o perioadă de 3 ani cu rata dobânzii

9966 [12]

Answer:

960

Step-by-step explanation:

The simple interest formula is the following:

I = P*r*t

Where I is the interest generated after t years, P is the inicial value and r is the rate of interest.

In this case, we have that the inicial value is P = 4000, the rate of interest is r = 8% = 0.08 and the amount of time invested is t = 3 years.

So, the interest will be:

I = 4000*0.08*3 = 960

3 0

3 years ago

What is the answer? please help

amid [387]

Answer:

solution,

A(2,7)---------> (X1,y1)

B(6,3)--------->(x2,y2)

now,

 $ab = ( \frac{x1 + x1}{2} \: , \frac{y1 + y2}{2} ) \\ = (\frac{2 + 6}{2} \: , \frac{7 + 3}{2} ) \\ = ( \frac{8}{2} \:, \frac{10}{2} ) \\ = (4 ,\: 5)$ 

hope this helps...

Good luck on your assignment...

7 0

3 years ago

Read 2 more answers