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Maurinko [17]
3 years ago
13

Prove that the Greatest Integer Function f: R -> R given by f(x) = [x], is neither one-once nor onto, where [x] denotes the g

reatest integer less than or equal to x.
Mathematics
1 answer:
Karo-lina-s [1.5K]3 years ago
8 0
F: R → R is given by, f(x) = [x]
It is seen that f(1.2) = [1.2] = 1, f(1.9) = [1.9] = 1
So, f(1.2) = f(1.9), but 1.2 ≠ 1.9
f is not one-one

Now, consider 0.7 ε R
It is known that f(x) = [x] is always an integer. Thus, there does not exist any element x ε R such that f(x) = 0.7

So, f is not onto
Hence, the greatest integer function is neither one-one nor onto.

The answer was quite complicated but I hope it will help you.
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If h = 21 units and r = 7 units, what is the volume of the cone shown above?
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Pete is a politician. He claims that 32% of the households in his district have total household incomes below the poverty level.
victus00 [196]

Answer:

z=\frac{0.3867 -0.32}{\sqrt{\frac{0.32(1-0.32)}{225}}}=2.145  

For a bilateral test the p value would be:  

p_v =2*P(z>2.145)=0.0320  

Step-by-step explanation:

Information given

n=225 represent the sample selected

X=87 represent the households with incomes below the poverty level

\hat p=\frac{87}{225}=0.3867 estimated proportion of households with incomes below the poverty level

p_o=0.32 is the value that we want to test

z would represent the statistic

p_v represent the p value

System of hypothesis

We want to check if the true proportion is equal to 0.32 or not.:  

Null hypothesis:p=0.32  

Alternative hypothesis:p \neq 0.32  

The statistic is given bY:

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

Replacing we got:

z=\frac{0.3867 -0.32}{\sqrt{\frac{0.32(1-0.32)}{225}}}=2.145  

For a bilateral test the p value would be:  

p_v =2*P(z>2.145)=0.0320  

4 0
3 years ago
What is the factored form of x^12x^18+1
AlladinOne [14]
I think the answer is 16x^2+1 
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Taylor was asked to solve the system of linear equations
yarga [219]
Id take a guess and say line 1 because the rest looks correct
4 0
3 years ago
If someone could please answer all 3 points (20 points)
Aleksandr [31]

The missing parts of the table for the function are 49, 1 and 49 respectively

<h3>How to complete the missing parts of the table?</h3>

An exponential function is a type of function which involves exponents. A simple exponential function is of the form y = bˣ

Given:  the exponential function y = (1/7)ˣ

In order to find the missing parts, we have to substitute the relevant values into the function. Thus:

For x = -2:

y = (1/7)ˣ

Substitute x = -2 into the function:

y = (1/7)⁻² = 49

For x = 0:

y = (1/7)ˣ

Substitute x = 0 into the function:

y = (1/7)⁰ = 1

For x = 2:

y = (1/7)ˣ

Substitute x = 2 into the function:

y = (1/7)² = 1/49

The missing part is 49

Therefore, the missing parts of the table are 49, 1 and 49 respectively

Learn more about exponential function on:

brainly.com/question/27161222

#SPJ1

7 0
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