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VikaD [51]
3 years ago
8

Is 18 a divisor of 6?

Mathematics
1 answer:
Reptile [31]3 years ago
5 0
Yes it is because 18÷6 is 3 and 6×3=18
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Prove the function f: R- {1} to R- {1} defined by f(x) = ((x+1)/(x-1))^3 is bijective.
Eduardwww [97]

Answer:

See explaination

Step-by-step explanation:

given f:R-\left \{ 1 \right \}\rightarrow R-\left \{ 1 \right \} defined by f(x)=\left ( \frac{x+1}{x-1} \right )^{3}

let f(x)=f(y)

\left ( \frac{x+1}{x-1} \right )^{3}=\left ( \frac{y+1}{y-1} \right )^{3}

taking cube roots on both sides , we get

\frac{x+1}{x-1} = \frac{y+1}{y-1}

\Rightarrow (x+1)(y-1)=(x-1)(y+1)

\Rightarrow xy-x+y-1=xy+x-y-1

\Rightarrow -x+y=x-y

\Rightarrow x+x=y+y

\Rightarrow 2x=2y

\Rightarrow x=y

Hence f is one - one

let y\in R, such that f(x)=\left ( \frac{x+1}{x-1} \right )^{3}=y

\Rightarrow \frac{x+1}{x-1} =\sqrt[3]{y}

\Rightarrow x+1=\sqrt[3]{y}\left ( x-1 \right )

\Rightarrow x+1=\sqrt[3]{y} x- \sqrt[3]{y}

\Rightarrow \sqrt[3]{y} x-x=1+ \sqrt[3]{y}

\Rightarrow x\left ( \sqrt[3]{y} -1 \right ) =1+ \sqrt[3]{y}

\Rightarrow x=\frac{\sqrt[3]{y}+1}{\sqrt[3]{y}-1}

for every y\in R-\left \{ 1 \right \}\exists x\in R-\left \{ 1 \right \} such that x=\frac{\sqrt[3]{y}+1}{\sqrt[3]{y}-1}

Hence f is onto

since f is both one -one and onto so it is a bijective

8 0
3 years ago
What is the value of x?<br> 16<br> 34
lord [1]

Answer:30

Step-by-step explanation:

7 0
2 years ago
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What is the lowest common denominator of 4,5,6,7,8 and 9?
Readme [11.4K]

Answer:

least common is 1!

Step-by-step explanation:

plz mark me brainliest

5 0
3 years ago
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A family plans to water ski at a local lake. If the temperature outside is 30 degrees C, what is the temperature in degrees F? U
Sphinxa [80]
30 degrees C = 86 degrees F
8 0
2 years ago
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Each day a small business owner sells 200 pizza slices at $3.00 per slice and 85 sandwiches at $2.50 each. Business expenses com
klio [65]

How much are the owner's expenses for 10 days?

10 * 130 = $1300

 

How much money does the owner make selling pizzas per day?

200 * 3 = $600

 

How much money does the owner make selling sandwiches per day?

85 * 2 = $170

 

In one day, the owner sells 600 + 170 = $770 worth of pizza and sandwiches

 

Over the course of ten days, that is 10 * 770 = $7700

 

Profit = revenue - cost = 7700 - 1300 = $6400


There ya go

5 0
3 years ago
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