Use f(x) = 2x − 3 and g(x) = 4 − x2 to evaluate the expression.
(a) (f ∘ g)(x)
(b) (g ∘ f)(x)

Answers

Answer 1

The resulting expressions for [tex](f\,\circ\,g)(x)[/tex] and [tex](g\,\circ\,f)(x)[/tex] are [tex]5- 2\cdot x^{2}[/tex] and [tex]-4\cdot x^{2} + 12\cdot x -5[/tex], respectively.

A composition is a operation two functions in which the independent variable of the first function is substituted by the entire second function. In other words, we have the following expressions:

[tex](f\,\circ\,g) (x) = f(g(x))[/tex] (1)

[tex](g\,\circ \,f)(x) = g(f(x))[/tex] (2)

If we know that [tex]f(x) = 2\cdot x - 3[/tex] and [tex]g(x) = 4 - x^{2}[/tex], then we have the following compositions:

[tex](f\,\circ\, g) (x) = 2(4-x^{2})-3[/tex]

[tex](f\,\circ\,g)(x) = 5-2\cdot x^{2}[/tex]

[tex](g \circ f) (x) = 4 - (2\cdot x-3)^{2}[/tex]

[tex](g\,\circ f) (x) = -4\cdot x^{2} +12\cdot x -5[/tex]

The resulting expressions for [tex](f\,\circ\,g)(x)[/tex] and [tex](g\,\circ\,f)(x)[/tex] are [tex]5- 2\cdot x^{2}[/tex] and [tex]-4\cdot x^{2} + 12\cdot x -5[/tex], respectively.

We kindly invite to check this question on composition between functions: https://brainly.com/question/15070966


Related Questions

Answer the question below

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Answer:

box A.

Step-by-step explanation:

im not really sure

Answer:

BOX A

Step-by-step explanation:

The more of something there is, the more heavier it is.

If mVSR 8x + 18, find the value of x so that US I VS.

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Answer:

x = 9

Step-by-step explanation:

must be 90deg in order to be perpendicular.

90 = 8x + 18

72 = 8x

9 = x

Help im stuck of this assignment

Answers

Answer:

48÷8, -36÷-12

Step-by-step explanation:

In a river, a trout passed beneath a woman who was swimming at 1,800 centimeters per minute. The trout swam 8,000centimeters directly upstream at a constant velocity. It swam that distance in 0.8minutes. What was the trout's velocity?

Write your answer as a whole number.

centimeters per minute upstream

Answers

Answer:

It would approximately be 3.73 m/h

Step-by-step explanation:

0.8 mins is 48 seconds

I then divided 8000 by 48 seconds to see how many cm it traveled per second.

It traveled 166.666666667 cm per second

I then converted cm to feet

so it was 5.468066491699474 feet per second

I then converted feet to miles, so it was 0.0010356186537309611598 miles per second.

Then I multiplied it by 60 so it was 0.06213711922 miles per minute.

Finally I multiplied it by 60 again to make it 3.72822715343 miles per hour.

I rounded it to the nearest hundredth making it 3.73 m/h

A group of friends wants to go to the amusement park. They have no more than $150
to spend on parking and admission. Parking is $13.50, and tickets cost $22.75 per
person, including tax. Write and solve an inequality which can be uused to determine
X, the number of people who can go to the amusement park.
FEE
Inequality:

Answers

Answer:

22.75x + 13.50 = 150

Step-by-step explanation:

the temperature dropped 4°c every hour for 5 hours. write an integer that represents the change in temperature

Answers

Answer:

20°C

Step-by-step explanation:

To find the change in temperature, we can multiply the values given.

4 * 5 = 20°C

Best of Luck!


Student Council plans on selling fresh hamburgers at the homecoming game. They
bought 40 lbs of ground chuck to use to make burgers and each burger uses 0.25 lbs
of chuck to make. What is the most amount of burgers they can sell at the game

Answers

Answer:

Student Council can make at the most 160 fresh burgers.

Step-by-step explanation:

Take 0.25 and divide it by 40.

0.25 / 40 = 160

Which statement about this equation is true?
2x + 4 = 2(x + 2)

Answers

Answer:

number 3 is right

Step-by-step explanation:

this equation has infinitely many solutions

What is the slope of the line

Answers

Answer:

3/3=1/1=1 is the slope

Step-by-step explanation:

the rise is 3 and the run is 3

Hope it helps!

The difference between two positive numbers , 12/(x + 1) and 12/x , 1. () Form an equation in x and show that it reduces to x ^ 2 + x - 12 = 0 . (ii) Solve the equation x ^ 2 + x - 12 = 0 . () Hence , find the two numbers .

Answers

Answer:

Step-by-step explanation:

12

prove that 5^(2n - 1) is divisible by 8​

Answers

Your teacher must have made a typo somewhere. The expression 5^(2n-1) is not divisible by 8.

The expression 5^(2n-1) is composed of 2n-1 copies of "5" multiplied together. The key here is that 5 is the only unique prime factor of this number.

On the other hand, 8 = 2*2*2 = 2^3 showing that 2 is the only prime factor for this number. At this point, we can see that there's no way that 5^(2n-1) is divisible by 8. It all comes down to the clash of the primes 5 and 2 not matching up, and having nothing in common.

Let's consider a few concrete examples:

If n = 1, then 5^(2n-1) = 5^(2*1-1) = 5^1 = 5 which is not divisible by 8. The number 5/8 = 0.625 isn't an integer.If n = 2, then 5^(2n-1) = 5^(2*2-1) = 5^3 = 125 which is also not a multiple of 8. The number 125/8 = 15.625 isn't an integer.

I'll let you try other natural numbers for n, and you'll find that [tex]\frac{5^{2n-1}}{8}[/tex] isn't an integer.

There are 16 boys and 18 girls in a grade 6 math class . write the ratio of girls to boys in words as simply as possible

Answers

Answer:

8:9 = eight to nine

Step-by-step explanation:

16:18 - divide each by 2 in order to simplify

= 8:9

Determine the average speed of the monorail, in miles per hour, over each segment of the route. Round each speed to the nearest tenth of a mile per hour

Answers

Answer:

show everything

Step-by-step explanation:

copy and paste all of all of the problem

Divide and express in the form of a complex number a + b i.
(-1 - 2i) / (- 4 + 3i)

Answers

Answer:

-2 / 25 + (11 / 25) i

Step-by-step explanation:

Hope this helps :)

Michael walks a group of dogs 3 miles every day. The graph below shows the relationship between the number of dogs in the group and the distance he walks the dogs each day​

Answers

Can you please add the graph, plus the question?

please help me solve x please

Answers

Answer:

x = 5

Step-by-step explanation:

The exterior angle theorem states that the measure of each exterior angle of a triangle is equal to the sum of the opposite and non-adjacent interior angles.

In the given problem, the exterior angle is < B, and the non-adjacent interior angles are < D and < C.

Given that:

< B = 12x + 8

< D = 8x + 8

< C = 20°

Set up the following formula to solve for x:

(8x + 8) + 20 = 12x + 8

Combine like terms:

8x + 28 = 12x + 8

Subtract 8 from both sides:

8x + 28 - 8 = 12x + 8 - 8

8x + 20 = 12x

Subtract 8x from both sides:

8x - 8x + 20 = 12x - 8x

20 = 4x

Divide both sides by 4 to solve for x:

20/4 = 4x/4

5  = x

Therefore, x = 5.

this is like my 4th time posting this can someone plz help me

Answers

Answer:

35 degrees

Step-by-step explanation:

All angles of a triangle add up to 180 degrees.

180-120-25 = ?

? = 35

Answer:

35

Step-by-step explanation:

Simplify 3 10 +7 15- 6 10 -4 15
O 3/10-315
O 315-3110
O 3130 -3120
O 3120-3130

Answers

Answer:

B

Step-by-step explanation:

geometry!!


JL has endpoints J(8,10) and L(20,5). Point K has coordinates (13,9). What is the length of JL?

Answers

The length of line JL which has endpoints J(8,10) and L(20,5) is; JL = 13.

According to the question, we are required to determine the length of line JL.

However, the coordinates of the end points of line JL are given as;

Point J; (8,10)

Point L; (20,5).

The length of line JL is given by Pythagoras theorem as;

JL = √(20-8)² + (5-10)²

JL = √ 12² + (-5)²

JL = √ 144 + 25

JL = √169

JL = 13.

Therefore, the length of line JL which has endpoints J(8,10) and L(20,5) is; JL = 13.

Read more:

https://brainly.com/question/13502098

A laptop has a listed price of $503.98 before tax if the sales tax rate is 7.5% find the total cost of the laptop with sales tax included

Answers

Answer:

The tax would be roughly $37.79, which means the laptop would be overall $541.77.

Please help me solve this

Answers

Answer:

Step-by-step explanation:

This number is much larger than 1. You need to start at the decimal and move left (that's how scientific notation works for numbers larger than 1.)

So the answer is 1.0054 * 10 ^7

The person doing this started at the 1 and moved right until he/she hit the decimal. Wrong direction.

Rachel can finish the job in 5 hours, while Carl can finish the same job in 8 hours. How long will it take them to finish the job together?PLS ANSWER ASAP WILL MARK BRAINLIEST IF CORRECT!!!!

Answers

5-7 hours i think, not 100% sure

Step-by-step explanation:

if you have any answer choices can you please list them? I'm not sure if this is correct but I'm guessing it'll take them both 5ish hours. Since Rachel can finish it in 5 hours but Carl takes longer, either they'll get it done in 5 hours or may it'll take a longer like 6 hours if Carl slows Rachel down. hope this helps!

Answer: 3 hours

Step-by-step explanation:

If she can do it in 5 and he, in 8 then subtract 5-8 and you get 3. Together they can complete this in 3 hours. Have a great day!

Stephen was thinking of a number. Stephen divides by 5 then adds 1 to get an answer of 21. Form an equation with
x
from the information.

Answers

Answer:

x/5 +1 = 21

Step-by-step explanation:

x is your variable. first step is divided by 5, so you put x/5. then it says add 1 so simply add it on to the equation x/5 + 1. the entire equation equals to 21 so you put the equal sign after x/5 +1 =21

Dilate XYZ at Center 0 and a scale factor of 12
0
2
Dilate FGHJ at center Rand

Answers

Where is the diagram?

hELP asap


39.67 + 18.41

Answers

Answer:

58.08

Step-by-step explanation:

Answer:

58.08

Step-by-step explanation:

39.67+18.41=58.08

A test is worth a total of 150 points and contains 70 questions. Some of the questions are worth 2 points and some are worth 4 points.
The test has
questions worth 2 points and
questions worth 4 points.

Emma answered a certain number of questions correctly and scored 100 points. If she answered 46 questions worth 2 points correctly, the number of questions worth 4 points she answered correctly is
.

Answers

Answer:

[tex]46 \times 2 = 92 \: points \\ 100 - 92 = 8 \: points \\ 4 \times 2 = 8 \\ two \: of \: the \: 4 \: points \: questions \: \\ were \: answered \: correctly[/tex]

X/2 -5=20 please give details

Answers

Answer: x=50

how?

[tex]\frac{x}{2}[/tex] - 5= 20 (first ADD 5 with 20 whatever you do on one side you have to do it to the other) so that gives us:

[tex]\frac{x}{2}[/tex]=25 (we see that 2 is being divided by x and we want X alone so the inverse of division is MULTIPLICATION)

25 x 2= 50

therefor the x=50

if i read 50 pages in 40 minutes how many pages do i read a minute

Answers

Answer:

You are reading 1 1/4 page/minute.

Step-by-step explanation:

Answer: 50/40= 1.25 pages

What is the value of W in a exterior angle theorem

Answers

Answer:

26

Step-by-step explanation:

The sum of two interior angles in a triangle is equal to an exterior angle that is supplementary to the third interior angle.

so:

30 + 2w - 8 = w + 48

22 + 2w = w + 48 export like terms to the same side of the equation

2w - w = 48 - 22 subtract

w = 26

What is the slope of line segment betweem the points (-1,-1) and (-2,-4)

Answers

Answer: 3

Step-by-step explanation:

Slope formula: (y2 - y1)/(x2 - x1)

(-4 -(-1))/(-2-(-1)

(-4+1)/(-2+1)

-3/-1

= 3

For detailed, step-by-step explanations you can visit my fiverr account: kesja_

I provide detailed explanations for math questions for as little as $1!

Answer:

hope you like my answer its -3

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