Answers
The composite functions are listed below:
g ° f(3) = 29 g ° f(x + 1) = 2 · x² - 1 h ° g (- 3 · x) = - 36 · x - 36 f ° g (- 2 - t) = 73 + 72 · t + 16 · t² f ° g (x²) = 3 · x² + 17How to evaluate composite functions
In this problem we find five cases of composite functions, each of which has to be evaluated. A composition between the two functions f and g is defined below:
f ° g(x) = f ( g(x) )
Now we proceed to evaluate each of the five cases by using algebra properties and the definition of the composition of functions:
Case 1
g ° f(3) = g( f(3) )
g ° f(3) = 4 · (2 · 3 + 2) - 3
g ° f(3) = 4 · 8 - 3
g ° f(3) = 29
Case 2
g ° f(x + 1) = g( f(x + 1) )
g ° f(x + 1) = 2 · [(x + 1)² - 2 · (x + 1)] + 1
g ° f(x + 1) = 2 · (x² + 2 · x + 1 - 2 · x - 2) + 1
g ° f(x + 1) = 2 · (x² - 1) + 1
g ° f(x + 1) = 2 · x² - 1
Case 3
h ° g (- 3 · x) = h( g (- 3 · x) )
h ° g (- 3 · x) = 3 · [4 · (- 3 · x) - 3]
h ° g (- 3 · x) = 3 · (- 12 · x - 12)
h ° g (- 3 · x) = - 36 · x - 36
Case 4
f ° g (- 2 - t) = f( g (- 2 - t))
f ° g (- 2 - t) = [4 · (- 2 - t) - 2]² + 1 + 2 · [4 · (- 2 - t) - 2]
f ° g (- 2 - t) = (- 8 - 4 · t - 2)² + 1 + 2 · (- 8 - 4 · t - 2)
f ° g (- 2 - t) = (- 10 - 4 · t)² + 1 + 2 · (- 10 - 4 · t)
f ° g (- 2 - t) = 100 + 80 · t + 16 · t² + 1 - 20 - 8 · t
f ° g (- 2 - t) = 73 + 72 · t + 16 · t²
Case 5
f ° g (x²) = f( g(x) )
f ° g (x²) = 3 · (x² + 4) + 5
f ° g (x²) = 3 · x² + 12 + 5
f ° g (x²) = 3 · x² + 17
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Related Questions
6th grade math help me pleasee
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1. Kris
2. Katie
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help please i’m stuck lol
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Answer:
The answer for this is x=-5
Answer:
x=-5
Step-by-step explanation:
-4x+1=21
move the 1 to the right side and subract it so it will turn into -4x=20
divide -4 to get the x by itself and then you will get x=20/-4 this will now divide and be x=-5
Use the equation y = x - 2 and perform a reflection over the x-axis. Write an equation in 2
1
slope intercept form that represents the new line.
Answers
Answer:
Please check the explanation.
Step-by-step explanation:
Given the equation
y=x-2
We know that Reflecting over the x-axis inverts the sign of the y-coordinate.
Thus, after reflecting over the x-axis, the equation would be:
-y = x - 2
Now, writing the equation in the slope-intercept form
y=mx+b
where
m is the slope and b is the y-interceptso the equation in the slope-intercept form
-y = x - 2
y = -x + 2
Here,
The slope = m = -1The y-intercept = b = 2Cheryl paid $37.20 for 12 gallons of ice cream for a school picnic. how much would 1 quart of ice cream cost? group of answer choices $4.10 $0.68 $0.78 $3.10
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Cheryl, that paid $37.20 for 12 gallons of ice cream for a school picnic would pay $0.78 for 1 quart of ice cream
To solve this problem, we have to state the equation using the information of the problem
Information about the problem:
Payment= $37.20Amount= 12 gallons1 quart cost=?Converting the amount unit from gallon to quart, we get:
12 gallons * (4 quart / 1 gallon) = 48 quarts
12 gallons are equivalent to 48 quarts
Calculating how much would cost 1 quart of ice cream:
1 quart cost = payment / amount(quart)
1 quart cost = $37.20 / 48 quarts
1 quart cost = $0.78
What are algebraic operations?We can say that they are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
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Is the last option correct?
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Answer:
yes it is
Step-by-step explanation:
PLEASE NEED HELP NOW WILL GIVE BRAINLIEST
What is the value of B?
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61 + 58 = 119
180 - 119 = 61
So, you’re answer would be 61 degrees. Hope that helped :)
Some one help pleaseeeee its very easy
Answers
Answer:
the last one 5/6
Step-by-step explanation:
Answer:
5/6
I hope this helps!
PLEASE I NEED HELP FOR THIS TEST
Simplify the difference. Write your answer in standard form.
2) (8r - 4r + 8) - (5r - 8 + 7r")
A) -24r + 3r + 16
B) 3r + 13r + 16
C) -11p+ 3r + 16
D) -317 + 3r + 16
Answers
Answer:
- 11r³ + 3r + 16
Step-by-step explanation:
( 8r - 4r³ + 8 ) - ( 5r - 8 + 7r³ ) =
= 8r - 4r³ + 8 - 5r + 8 - 7r³ =
= - 11r³ + 3r + 16
Find the measure of the missing angle
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Answer:
154
Step-by-step explanation:
180-26=154
Jai bought 9 chicken wings for $20.70. How much does each wing cost?
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Step by step: $20.70 divided by the 9 wings
Help me with this problem please
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Answer:
the answer is B
Step-by-step explanation:
the length of one side of a rectangle is p cm and width is 3(p-2) cm the perimeter is 44 cm find the length and width of rectangle
Answers
Answer:
Length = 7cm, Width = 15cm
Step-by-step explanation:
Length = p
Width = 3(p-2)
= 3p-6
Perimeter = length + width + length + width
= p + 3p-6 + p + 3p-6
= 8p-12
8p - 12 = 44
Isolate 8p.
8p = 44+12
= 56
Find p.
p = 56 ÷ 8
p = 7
Length = 7cm
Width = 3(7)-6
= 21-6
= 15cm
add or subtract the following fractions. write in simplest form.
3/4 - 3/10
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Answer:
I got 9/20
Hope that helps!
A car park space needs 8 square metres for 1 car. just considering the spaces for parking, what dimensions for a car park would be needed for 60 cars
Answers
The dimensions of a car park for 60 cars is: 480 m^2
To solve this exercise we have to do a mathematical operations of multiplication with the given information.
Information about the problem:
car park space = 8 m^2/cardimensions for a car park (60 cars) = ?To know the dimensions for the car park of 60 cars we have to do the following multiplication:
dimensions for a car park (60 cars) = car park space * 60 cars
dimensions for a car park (60 cars) = 8 m^2/car * 60 cars
dimensions for a car park (60 cars) = 480 m^2
What is multiplication?It is a mathematical operation that consists of adding the same number, called the multiplicand, as many times as indicated by another number, called the multiplier. The result is called the product.
Example: 2+2+2= 6 is equal to say 2*3= 6
Multiplied * multiplier = product
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what is 30 percent of 210
Answers
Answer:
63
Step-by-step explanation:
Can anyone please help me with this. It’s late and I need help asap :)
Answers
Answer:
I think they're both always but I'm not sure
Pls help will give brainliest to who is Wright
Answers
Answer:
24
Step-by-step explanation:
Hope this helps! :3
plz mark as brainliest!
Answer:
The answer is 24 :)
What is the transformation from ΔA'B'C' to ΔA''B''C'' ?
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2. 180 degrees
3. reflection across y = x
15−2x=3x what is x solved for
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15-2x=3x
15=5x
3=x
Translate the phrase into an algebraic expression.
3 times b
Answers
Answer:
3b
Step-by-step explanation:
It`s just . . . 3b lol
When numbers and variables multiply, they are put in the form of (integer)(variable). They phrase can only be further simplified if there is a number substitution for b.
Erin owns 48 movies on DVD. Three eighths of the movies are comedies, 1/3 are dramas, 1/4 are action adventure, and the rest are science fiction. What part of her movie collection is science fiction?
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Ezra has two weeks to sell popcorn to earn money for camp. For each unit of popcorn that he sells, Ezra will earn $5. He wants to earn at least $250
. During the first week he earned $105.
How many units of popcorn must Ezra sell in the second week to earn at least $250 in the two weeks combined?
Answers
in the first week he sold 21 units of popcorn
he needs to sell 50 units in all
so 50-21= 29
he needs to sell 29 more units of popcorn
The number of units that needs to be sold to earn at least $250 is 20.
What is inequality?
It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
The minimum amount that needs to be earned = $250
One unit cost = $5
The amount earned in the first week = $105
Number of units = x
The number of units to sell in the second week.
150 + 5x ≥ 250
5x ≥ 250 -150
5x ≥ 100
x ≥ 20
Thus,
20 units need to be sold to earn at least $250.
Learn more about inequalities here:
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A triangle has vertices (2, 1), (5, 1), and (5,5). What is the length of the longest side of the triangle?
HELPPPP !!! I ONLY HAVE 30 MINUTES LEFT
Answers
Answer:
5,5
Step-by-step explanation:
it has the longest side
there are 20% more goblins than wizards in magic club there are 120 goblins in magic club
Answers
Answer:
Final Answer: There are 100 wizards in the magic club
Step-by-step explanation:
Since this question is asking for how many wizards are in magic club, we can represent wizards with the variable "w"
w = wizards
Next, we know that there are 120 goblins and that there are 20% more goblins than wizards in magic club.
120 = w + 20%w
120 = w + 0.2w
(percentages are just the percent/100)
120 = 1.2w
1200 = 12w
100 = w
HELP!!!! WILL MARK BRAINLIEST!!!!!!
Answers
Answer: The answer is 9 because the equations represent the same expression but just in different forms.
Step-by-step explanation:
Pls help I need the answer quick
Answers
49
..............
Amber has a dog walking business. she walks a golden retruever 1.8 miles each work day for a week. How many miles does Amber walk the golden retreiver? plz tell me i will give you brainlist
Answers
Answer:
12.6
Step-by-step explanation:
Answer:9 miles
Step-by-step explanation:
5 working daya x 1.8 miles = 9 miles
Step-by-step explanation: 1.8 x 7
Part A: determined if the triangles are similar?
Part B: complete the similarity statement, if they are not similar, type Not Similar.
Answers
Answer:
please pleasehelp help me me my question
A board 10 feet long is cut into three pieces. one piece is 1 foot longer than the shortest piece and 2 feet shorter than the longest piece. how long is each piece?
Answers
Answer:
3:2:5
Step-by-step explanation:
x+1:x:x+3
x=2
10-4=6/3=2
HELPPP!! What is the slope of a line that is perpendicular to
y = - 3x + 10 ?
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Answer:
the answer is 1/3. hope it help