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
laila [671]
3 years ago
9

F ( x ) = x − 3 x , g ( x ) = x + 3 , h ( x ) = 2 x + 1 , ( g ⋅ h ⋅ f ) ( x )

Mathematics
1 answer:
DiKsa [7]3 years ago
8 0

Composing functions just means to feed the ouput of the inner one as the input for the outer one.

So, the following writings are equivalent:

(g\circ h \circ f)(x) = g(h(f(x)))

Using the second form, we can see that the first thing to do is to compute f(x), which is given:

f(x) = x-3

This means that we can update the fomula:

(g\circ h \circ f)(x) = g(h(f(x))) = g(h(x-3))

So, now we have to compute h(x-3). Given h(x)=2x+1, we know that h doubles the input and adds one. In this case, the input is x-3, so we have to double this and add one:

h(x-3) = 2(x-3)+1 = 2x-6+1 = 2x-5

So, we have

(g\circ h \circ f)(x) = g(h(f(x))) = g(2x-5)

Similarly, from g(x) = x+3, we understand that g just adds 3 to the input. In this case, the input is 2x-5, so we'll add 3 to this quantity:

g(2x-5) = (2x-5)+3 = 2x-2

So, we finally have

(g\circ h \circ f)(x) = g(h(f(x))) = 2x-2

You might be interested in
Find the area of shaded region.
Rudiy27

Hey there mate ;),

Area of The shades region is <u>3098 m^2</u>

The solution is attached as picture. Please check.

<em>Answered</em><em> </em><em>by</em><em> </em><em>Benjemin</em>

6 0
2 years ago
Is the negative square root of 9 rational or irrational ​
Nana76 [90]

Answer:

Rational

Step-by-step explanation:

-9 is rational because 9 is a perfect square and all perfect squares are rational.

6 0
3 years ago
I need help with HW it is hard (repost i forgot picture)
creativ13 [48]

Answer:

b 8 hours

Step-by-step explanation:

1/4 is 2 so 2/4 is 4 and we know 3/4 is 6 so 4/4 is 8 which is the answer

4 0
3 years ago
How much water do you need to add to make each concentration?<br> 1% sugar syrup using 12 g sugar
yulyashka [42]

Answer:

1188 grams of water

Step-by-step explanation:

x is the grams of water

so total is 12+x grams

sugar/total is 12/12+x

and 1% ratio is 12/12+x=1/100

so x would be 1188 grams of water.

6 0
2 years ago
4. Of 100 students surveyed, 32
Mrac [35]

Answer:

16 students

Step-by-step explanation:

40 kids like only carrots and 40% of a hundred is 40%, so out of the 40 students that will be surveyed only 40% will like only carrots. 40% of 40 is 16

8 0
3 years ago
Other questions:
  • 3 = x - 8<br> I need this right now plz
    9·2 answers
  • Can someone help me with this?
    10·1 answer
  • Your six month old baby has doubled his birth weight, is grasping objects and pulling them to his mouth, and seems hungry all th
    5·2 answers
  • The sum of three consecutive numbers is 72. What is the middle number?
    12·2 answers
  • |3x|=9 what's the answer and the breakdown of this problem?
    8·2 answers
  • Which graph is correct
    13·1 answer
  • The masked singer traveles 250 miles in 5 hours to get to los angeles for a show. How many miles did the singer travel in an hou
    12·2 answers
  • Simplify. (-3x - 2) - (7x + 9)
    13·1 answer
  • Factor the algebraic equation<br> 36a+20
    8·2 answers
  • Please help with math problem give a good rating and 5 stars
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!