1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Softa [21]
3 years ago
9

Given the functions f(x) = 3x and g(x) = x² + 1, find [(gºf)(x)]- [(fºg)(x)].

Mathematics
1 answer:
Ipatiy [6.2K]3 years ago
7 0

Answer:

6x^2 - 2

Step-by-step explanation:

plug in f(x) into the g(x) formula given

g(f(x)) = (3x)^2 + 1

simplify

= 9x^2+2

plug in g(x) into the f(x) formula given

f(g(x)) = 3(x^2+1)

distribute

= 3x^2 +3

set g(f(x)) - f(g(x))

(9x^2+2) - (3x^2+3)

carry the negative

9x^2+2-3x^2-3

simplify by combining like terms

6x^2-2

You might be interested in
Ava and Kelly ran a road race, starting from the same place at the same time. Ava ran at an average speed of 6 miles per hour. K
zalisa [80]
<h2>Hello!</h2>

The answer is:

It will took 0.375 hours for Ava and Kelly to be 3/4 miles apart.

<h2>Why?</h2>

To calculate how long after they start they will be 3/4 miles apart, we need to write two equations.

So, writing the equations, we have:

Calculations for Ava:

We have the following information,

v_{Ava}=6mph

Then, writing the equation,

x_{Ava}=x_{o}+v_{Ava}*t

x_{Ava}=x_{o}+v_{6mph}*t

Calculations for Kelly:

We have the following information,

v_{Kelly}=8mph

We need to calculate when Kelly will be 3/4 miles apart of Ava, so, it's position will be the Ava's position plus 3/4 miles.

Then, writing the equation,

x_{Ava}+0.75miles=x_{o}+v_{Kelly}*t

x_{Ava}+0.75miles=x_{o}+v_{8mph}*t

Now, substituting Ava's speed into the second equation, we have:

x_{o}+6mph*t+0.75miles=x_{o}+8mph*t

6mph*t+0.75miles=+8mph*t

8mph*t-6mph*t=0.75miles

2mph*t=0.75miles

t=\frac{0.75miles}{2mph}=0.375hours

Hence, we have that it will took 0.375 hours for Ava and Kelly to be 3/4 miles apart.

Have a nice day!

7 0
3 years ago
Read 2 more answers
A kite flying in the air has a 10-ft line attached to it. It’s line is pulled taut and casts a 7-ft shadow. Find the height of t
jasenka [17]

Answer:

If the kite has an 11 ft line attached to it and it casts an 8 feet shadow, we will have a rectangle triangle (see picture below).

To find the height x of the kite, we can apply the Pythagorean theorem.

x² = 11² - 8²

x² = 121 - 64

x² = 57

x =√57 Step-by-step explanation:

6 0
2 years ago
How to find the midpoint of a square
gtnhenbr [62]

The midpoint formula is

X1+X2 Y1+Y2

——— ———

2 2

4 0
3 years ago
Adam went on a shopping trip to Somerville. He purchased a set of dishes originally priced at
RUDIKE [14]

Answer:187.2

Step-by-step explanation:

Actual price $390

After 60% discount price will be 156

And Sales tax is 8% . Then the price of sales tax is $31.2.

156+31.2= $187.2

5 0
3 years ago
Eric took a test with 15 questions. he answered 2/5 of the questions correctly, how many did he get wrong?
givi [52]

Answer: 9

3/5's of 15 = 9

7 0
2 years ago
Other questions:
  • One thousand families were surveyed to determine the distribution of families by size
    13·1 answer
  • Which is the best unit to use for measuring the length of an eyelash millimeters C centimeters B meters or D kilometers
    5·1 answer
  • .25(1.2×3-1.25)+3.45
    5·1 answer
  • Is there enough information given to find the value of X. Explain your reasoning. Ty!
    12·1 answer
  • 2x+3=-7 what does x equal
    5·1 answer
  • Use the function from question #14 to solve: Water fills a community pool steadily all day, at a constant rate of 2.3 feet of wa
    9·1 answer
  • How do you find the square root of 25
    10·1 answer
  • Please please help help me with two questions!!
    7·1 answer
  • What is 3x + 9?<br> (Ignore this part, says the question needs to be more than 20 characters)
    13·2 answers
  • A line that includes the point (9, 10) has a slope of -1/9 what is its equation in point-slope
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!