MATHEMATICS MIDDLE SCHOOL

A. Use composition to prove whether or not the functions are inverses of each other. B. Express the domain of the compositions using interval notation.

Answers

Answer 1

Answer:

Given: $f(x) = (1)/(x-2)$

$g(x) = (2x+1)/(x)$

A.)Consider

$f(g(x))= f((2x+1)/(x) )$

$f((2x+1)/(x) )=(1)/(((2x+1)/(x))-2)$

$f((2x+1)/(x) )=(1)/((2x+1-2x)/(x))$

$f((2x+1)/(x) )=(x)/(1)$

$f((2x+1)/(x) )=1$

Also,

$g(f(x))= g((1)/(x-2) )$

$g((1)/(x-2) )= (2((1)/(x-2)) +1 )/((1)/(x-2))$

$g((1)/(x-2) )= ((2+x-2)/(x-2) )/((1)/(x-2))$

$g((1)/(x-2) )= (x )/(1)$

$g((1)/(x-2) )= x$

Since, $f(g(x))=g(f(x))=x$

Therefore, both functions are inverses of each other.

For the Composition function $f(g(x)) = f((2x+1)/(x) )=x$

Since, the function $f(g(x))$ is not defined for $x=0$ .

Therefore, the domain is $(-\infty,0)\cup(0,\infty)$

For the Composition function $g(f(x)) =g((1)/(x-2) )=x$

Since, the function $g(f(x))$ is not defined for $x=2$ .

Therefore, the domain is $(-\infty,2)\cup(2,\infty)$

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Is n=3 is a solution to the equation or 2n=6

Answers

opposite equation-->6/2
n=3
yes!

Yes. Of coarse! (This text is here to fill in 20 characters.)

Study the following statement:“Two intersecting lines cannot beperpendicular to the same line”. Check whether it is an equivalent version to
the Euclid’s fifth postulate.

Answers

Euclid's fifth postulate states that 'given any two lines and a transversal, if the angles on the same side of the transversal are less than 180 degrees they will meet on that side of the transversal'. The statement given here is that two intersecting lines cannot be perpendicular to the same line, i.e., parallel. This statement is stating that the co-interior angles of intersecting lines cannot be 90 degrees in measure, and it is almost equivalent to Euclid postulate 5.

(393,393,400,458,482,491,496,507,509,511) Which two measures of these data best describes the typical number of books that were returned to the library each week?

Answers

the mode (number that occurs most often) = 393 since it appears twice in this sequence

the mean (all the numbers added together and divided by the number of numbers in the sequence)= 393 +393 + 400 + 482 + 496 +507 +509 + 511= 3691

the median (when, the numbers are placed in order from lowest to highest, the middle number, or if there is a even amount of numbers, the two middle numbers added together than divided by 2) = 482 + 491 = 973/2 = 486.5

these three terms are all different forms of the average, although once you get to high school you will learn that they may not be very accurate when there is outliers, to which you will learn how to calculate the outliers and how to descaled them form your calculations :)

According to a survey, the population of a city doubled in 12 years.%. The population will grow to three times its current
The annual rate of increase of the population of this city is approximately
size in approximately
Roset

Answers

Answer:

5.78%

Step-by-step explanation:\

I hope this helps ^^

Convert the mixed number to an improper fraction. 2 7/10 A.14/10 B.27/10 C.34/10 D.37/10

Answers

The value of the mixed number is A = 27/10

What are Mixed Numbers?

A mixed number is a whole number, and a proper fraction represented together. A mixed number is formed by combining three parts: a whole number, a numerator, and a denominator. The numerator and denominator are part of the proper fraction that makes the mixed number.

Given data ,

Let the mixed number be represented as A

Now , the equation will be

A = 2 7/10 be equation (1)

On converting the mixed number to an improper fraction , we get

Multiply the whole number by the denominator and add the numerator to it to get the new numerator of the improper fraction

So , A = [ ( 2 x 10 ) + 7 ] / 10

On simplifying the equation , we get

A = 27/10

Hence , the mixed number to improper fraction is A = 27/10

To learn more about mixed numbers click :

brainly.com/question/2639375

#SPJ2

So, to make a mixed number into an improper fraction, you have to multiply the whole number by the denominator and then add the numerator o that number.
2 and 7/10:
2x10=20+7=27/10!
The answer would be B!
I hope this helps!

What is the average of 11, 16, and 18

Answers

The average of 11, 16, and 18 is 15.

To find the average of a set of numbers, you add all the numbers together and then divide the sum by the total count of numbers. In this case, you want to find the average of 11, 16, and 18.

Step 1: Add all the numbers together.

In this case, we have three numbers: 11, 16, and 18. To find the sum of these numbers, you simply add them together:

11 + 16 + 18 = 45

Step 2: Count the total number of values in the set.

In this case, there are three numbers in the set: 11, 16, and 18.

Step 3: Divide the sum by the total count of numbers.

To find the average, you divide the sum (45) by the total count of numbers (3):

Average = 45 / 3 = 15

So, the average of 11, 16, and 18 is 15.

To know more about average:

brainly.com/question/30180184

#SPJ2

The answer is 15. First, you would have to add all 3 of the numbers together and then once they are added, divide them by how many numbers you have altogether, which is 3. So, 11+16+18=45. 45 divided by 3 is 15.

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