Which statement describes function composition with respect to the commutative property? Given f(x) = x² – 4 and g(x) = x – 3, (f ∘ g)(2) = –3 and (g ∘ f)(2) = –3, so function composition is commutative. Given f(x) = 2x – 5 and g(x) = 0.5x – 2.5, (f ∘ g)(x) = x and (g ∘ f)(x) = x, so function composition is commutative. Given f(x) = x² and g(x)=StartRoot x EndRoot, (f ∘ g)(0) = 0 and (g ∘ f)(0) = 0, so function composition is not commutative. Given f(x) = 4x and g(x) = x², (f ∘ g)(x) = 4x² and (g ∘ f)(x) = 16x², so function composition is not commutative.
Answers
Answer:
The correct option are;
f(x) = x² - 4 and g(x) = x - 3, (f ο g)(2) = -3 and (g ο f)(2) = -3, so the function is commutative
Given f(x) = 4·x and g(x) = x², (f ο g)(x) = 4·x² and (g ο f)(x) = 16·x²
So the function is not commutative
Step-by-step explanation:
For the equations f(x) = x² - 4 and g(x) = x - 3, we have;
(f ο g)(x) = f(g(x)) = (x - 3)² - 4 = x² - 6·x + 9 - 4 = x² - 6·x + 5
At x = 2, we have;
(f ο g)(2) = f(g(2)) = 2² - 6×2 + 5 = - 3
Similarly, we have;
(g ο f)(x) = g(f(x)) = x² - 4 -3 = x² - 7
At x = 2, we have;
(g ο f)(2) = g(f(2)) = 2² - 7 = 4 - 7 = -3
Therefore, by commutative property, we have that the result of an operation does not change by changing the order of the operands such that we have;
a + b = b + a or a·b = b·a from which we have resolved also the following operation is commutative
(f ο g)(2) = (g ο f)(2)
Similarly given f(x) = 4·x and g(x) = x², (f ο g)(x) = 4·x² and (g ο f)(x) = 16·x²
So the function is not commutative
(f ο g)(x) = f(g(x)) = 4·x²
(f ο g)(x) = 4·x²
(g ο f)(x) = g(f(x)) = (4·x)² = 16·x²
(g ο f)(x) = 16·x²
∴ (f ο g)(x) = 4·x² ≠ (g ο f)(x) = 16·x²
(f ο g)(x) ≠ (g ο f)(x) the function is not commutative.
Answer:
DGiven f(x) = 4x and g(x) = x², (f ∘ g)(x) = 4x² and (g ∘ f)(x) = 16x², so function composition is not commutative.
Related Questions
what is the radius and circumference for this problem?
Answers
circumference is pie*d which is 26.71
Simplify.
7/11 -3/11
Answers
Answer:
4/11
Step-by-step explanation:
7/11-3/11
=>(7-3)/11
=>4/11
How are linear equations and linear inequality similar and different?
Answers
Answer:
The graph of linear inequalities include a dashed line if they are greater than or less than but not equal to. Linear equations, on the other hand, include a solid line in every situation. Moreover, linear inequalities include shaded regions whereas linear equations do not.
Step-by-step explanation:
Identify which equation represents a line parallel to the given equation 2x+5=25 asap please
Answers
Answer:
10
Step-by-step explanation:
2x(+5)=(25)< subtract 5 to each side
2x=20<divide 2 to 20
x=10
HELPPP PLEASEEEE I NEED THE ANSER Select the most precise and correct definition of parallel lines from among those that are given. Choose 1 answer: (Choice A) A Two distinct lines are parallel if one can be rotated to sit on top of the other. (Choice B) B Two distinct lines are parallel if they point in the same direction. (Choice C) C Two distinct lines are parallel if they are in the same plane and never intersect each other.
Answers
Answer:
C. Two distinct lines are parallel if they are in the same plane and never intersect each other.
Step-by-step explanation:
Parallel lines are best defined as 2 different lines that are in the same plane and will never intersect each other at any point in the graph.
They are always the same distance apart and will never touch.
So, C is correct
Answer:
C
Step-by-step explanation:
The very definition of parallel lines is that they have the same slope, if they have the same slope, they will never meet.
Write an equation of the parabola in vertex form.
Answers
Answer:
f (x) = a(x - h)2 + k, where (h, k) is the vertex of the parabola. ... When written in "vertex form": • (h, k) is the vertex of the parabola, and x = h is the axis of symmetry.
Answer:
y =0.25(x-4 )^{2}-1
Step-by-step explanation:
The formula of vertex form is as follows:
Y = a(x-h)^2+k
h = the x value for the vertex (in this case it is 4)
k = the y value for the vertex (in this case it is -1)
If you input these into the equation you are left with:
Y = a(x-4)^2-1
To find 'a' I just entered this equation into the Desmos calculator and messed around with the value until the y-intercept was (8,3)
I hope this was able to help! ^_^
7y ^3 −7x^3 +4−5+6−3x^3 +6x^3
Combine Like Terms
Answers
Answer:
-4x^3 + 7y^3 + 5
Step-by-step explanation:
7y^3 - 7x^3 + 4 - 5 + 6 - 3x^3 + 6x^3 Given
7y^3 - 7x^3 - 3x^3 + 6x^3 + 4 - 5 + 6 Rearrange
7y^3 - 4x^3 + 5 Combine the like terms
or
-4x^3 + 7y^3 + 5 Answer
The value of coins in the pockets of several students is recorded. What is the mean of the values: 10, 20, 35, 35, 35, 40, 45, 45, 50.60
a. 10 cents
b. 35 cents
c. 37.5 cents
d. 50 cents
Answers
Answer:
36.17
Step-by-step explanation:
Add all and divide by 9
Please solve -21+6x=3(3x-5)-x
Answers
Answer:
x=-3
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
−21+6x=3(3x−5)−x
−21+6x=(3)(3x)+(3)(−5)+−x(Distribute)
−21+6x=9x+−15+−x
6x−21=(9x+−x)+(−15)(Combine Like Terms)
6x−21=8x+−15
6x−21=8x−15
Step 2: Subtract 8x from both sides.
6x−21−8x=8x−15−8x
−2x−21=−15
Step 3: Add 21 to both sides.
−2x−21+21=−15+21
−2x=6
Step 4: Divide both sides by -2.
−2x
−2
=
6
−2
Dominic is driving on a long road trip. He currently has 10 gallons of gas in his car.
Each hour that he drives, his car uses up 1.25 gallons of gas. How much gas would be
in the tank after driving for 3 hours? How much gas would be left after t hours?
Answers
(1.25)t=gallons so 1.25 times the ammound of hours
Function h is a transformation of the parent exponential function, f(x)=2^x. h(x)=-3*2^x Which statement is true?
A. Function h is a vertical translation of function f. B. Function h is a reflection and a dilation of function f. C. Function h is a reflection and a translation of function f. D. Function h is a horizontal translation of function f.
Answers
Answer:
Function is a reflection and dilation of function f.
Step-by-step explanation:
A reflection gives the mirror image of function.
A function can be reflected about an axis by multiplying by -1.
To reflect function about the x-axis, multiply f(x) by -1 to get -f(x).
The correct option is: B. Function h is a reflection and a dilation of function f.
-----------------------
The functions are:
[tex]f(x) = 2^x[/tex]
[tex]g(x) = -3 \times 2^x[/tex]
It can be seed that g is f multiplied by -3.
The multiplication by a constant means that a dilation happened.Since the constant is negative, it means that a reflection also happened.In the image at the end of this question, it can be seen that the g, the blue graph, is a reflected and dilated version of f, the red graph.
Thus, the correct answer is:
B. Function h is a reflection and a dilation of function f.
A similar problem is found at https://brainly.com/question/17673148
What is the opposite value of -(-9) ?
Answers
Answer:
9
Step-by-step explanation:
two negatives make a positve
Answer:
-9
Step-by-step explanation:
Whenever you are given an expression, first look at it. Since there are two negative signs in the equation, they cancel out, leaving a nine. The opposite value most likely means that the sign is the opposite, so you end up with -9 as the value.
Which of the following equations is not written in general form?
2y = 7x - 19
2x + 5y - 9 = 0
5y - 9 = 0
Answers
Answer:
2y = 7x - 19
Step-by-step explanation:
can you accept my invite plz i wanna chat
and is it right
Asap please help me solve this Inequality?
[tex]3(x + 6) - 2(x + 2) \geqslant 10[/tex]
Answers
Answer:
[tex]x\geq -4[/tex]
Step-by-step explanation:
So we have the inequality:
[tex]3(x+6)-2(x+2)\geq 10[/tex]
First, distribute:
[tex](3x+18)+(-2x-4)\geq 10[/tex]
Combine like terms:
[tex](3x-2x)+(18-4)\geq 10[/tex]
Add:
[tex]x+14\geq 10[/tex]
Subtract 22 from both sides:
[tex]x\geq -4[/tex]
And we're done!
Point a and point b lie in the coordinate plane what is the midpoint between a (7,-5) and b (9,-1)
Answers
Answer:
(-3,8)
Step-by-step explanation:
formula
(y1+y2/2 ,X1+X2/2)
=(-5-1/2 ,7+9/2)
=(-6/2 ,16/2)
=(-3,8)
is -17.84 a rational number?
Answers
Answer:
yes
Step-by-step explanation:
-17.84 can be written as a/b where a and b are integers
-1784/ 100
This is a rational number
Find the coordinates of
the midpoint of AB with
endpoints A(3,7) and
B(0,2).
Thank you so much!
Answers
Answer:
[tex]M=(\frac{3}2},\frac{9}{2})[/tex]
Step-by-step explanation:
The midpoint is given by the formula:
[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
So we have the two endpoints A(3,7) and B(0,2).
Let's let (3,7) be x₁ and y₁ and let's let (0,2) be x₂ and y₂.
Therefore, our midpoint is:
[tex]M=(\frac{3+0}{2},\frac{7+2}{2})[/tex]
Add:
[tex]M=(\frac{3}2},\frac{9}{2})[/tex]
Or:
[tex]M=(1.5,4.5)[/tex]
And we're done!
Hope this helps!
Answer: (1.5,4.5)
Step-by-step explanation:
For midpoint i have a little cheer to remember the steps it goes," Midpoint, midpoint, what do you do? add them together and divide by two.
so using this problem as an example you would add the y coordinates and the x coordinates and get (3,9) then you divide X and Y by two.
So 3 divided by 2 is 1.5 so that is the X coordinate for the midpoint
and 9 divided by 2 is 4.5 so that is your Y coordinate for the midpoint.
Put it together and your answer is (3.5,4.5)
Find the missing dimensions. Use the scale factor 1 inch:12 feet. A plastic toy bird has a wingspan of 5 inches. What is the actual bird wingspan? USE NUMBERS ONLY Your answer
Answers
Answer: 60 feet
Step-by-step explanation:
Fron the question, we have been told to use a scale factor of 1 inch:12 feet. This simply means that 1 inch has been represented to 12 feet of the actual dimension.
We are further told that a plastic toy bird has a wingspan of 5 inches. The actual bird wingspan will therefore be 5 multiplied by 12 feet and this will be:
= 5 × 12 feet
= 60 feet
A plastic toy bird that has a wingspan of 5 inches has an actual bird wingspan of 60 feet
PLEASE HELP I HAVE A TON OF QUESTIONS AND EVERYTIME I REDO THIS ON THE TEST IT SAYS IM WRONG
Answers
Answer: the lengths of the line segments. hope this helps!
Step-by-step explanation:
b5c8 divided by b3c2
Answers
Step-by-step explanation:
b×5×c×8/b×3×c×2
5/3×4
the answer is 20/3
The endpoints of CD are C (4,6) and D(-1,-1). Find the coordinates of the midpoint M.
Coordinates of midpoint M: OD
6 HELP ME PLEASE I REALLY NEED HELP FAST 30 points
Answers
Answer:
M = (1.5, 2.5 )
Step-by-step explanation:
Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
[ [tex]\frac{1}{2}[/tex] (x₁ + x₂ ), [tex]\frac{1}{2}[/tex] (y₁ + y₂ ) ]
Here (x₁, y₁ ) = C(4, 6) and (x₂, y₂ ) = D(- 1, - 1) , thus
midpoint = [ [tex]\frac{1}{2}[/tex] (4 - 1) , [tex]\frac{1}{2}[/tex] (6 - 1 ) ] = (0.5(3), 0.5(5) ) = (1.5, 2.5 )
The product of 5 and the difference of 1 and a number.
Answers
Answer:
Simplify.
There's a product, so we are multiplying.
5 x...
The difference of one and a number. The number is a variable, since it could be any number.
1 - x
Let's combine them.
5 x (1 - x)
5(1 - x)
Hope this helped!
Mark this Brainliest, not that it matters.
Good luck :)
pls help
Lcm of 4 and 15?
least common multiple
Answers
=================================================
Explanation:
Multiply the two values to get 4*15 = 60
Then divide by the GCF 1 to get 60/1 = 60. The GCF being 1 means the result hasn't changed.
------
Another example would be: "Find the LCM of 6 and 8". We would first do 6*8 = 48, then divide by the GCF 2 to get 48/2 = 24. The LCM of 6 and 8 is 24.
Answer:
60
Step-by-step explanation:
A cope machine makes 32 copies per minute. How many copies does it make in 4minutes and 15 seconds?
Answers
Answer:
136
Step-by-step explanation:
4 times 32 = 128
32/4=8
128+8=136
Answer:
135
Step-by-step explanation:
1. divide 32 by 60 to get how many copies per second
[tex]32/60 = 0.533[/tex]
2. convert 4min and 15 sec to seconds
it is 255 seconds
3. Multiply copies per second by number of seconds
[tex]0.533(255) = 135.91[/tex]
4. Round down to whole number because you can't copy part of a paper
2.
aq - 8) = 23
Solve for q.
Sb please help me
Answers
Answer: q=31
Step-by-step explanation:
q -8 = 23 Add 8 to both sides
+8 +8
q = 31
1) 10x + 3y + 5x =
2) 2x + 7y+ 4x+6x? -
3) 9y+3y + 5x =
4) 2y + 7y + 4y + 6y' =
I
5) 8x + y - 2x =
6) x + 7y - 4y +9x?
7) 14x - 3x + 2 y = y + 3x -
8) 5y + 5y + 5y + 5x
What are the answer for these problems you need to simplify the expression by combining like terms
Answers
Answer:
Step-by-step explanation:
Terms with same variables are like terms
1) 10x + 3y + 5x
Here, 10x and 5x are like terms. so add them
10x + 5x + 3y = 15x +3y
2)2x + 7y +4x + 6x = 2x + 4x + 6x + 7y = 12x + 7y
3)9y+ 3y +5x = 12y +5x
4)2y +7y +4y +6y = 19y
5)8x + y - 2x = 8x -2x + y = 6x + y
6) x + 7y -4y +9x = x +9x + 7y - 4y = 10x + 3y
8) 5y +5y +5y +5x = 15y + 5x
Number 63 please help I’m desperate
Answers
8,45=845/100 dür.
[tex]\frac{845}{100} .\frac{1}{100}[/tex]
that is;
845/100000
namely
0,000845
My answer to the question is 0.0845.
You just need to move 2 times to the left...
Simplify the expression
(-3+4k) - (-2+ 7k)
Answers
Answer: −1−3k
Step-by-step explanation:
Distribute:
(−3+4k)−1(−2+7k)
(-3+4k)+{2-7k}
Eliminate redundant parentheses:
(−3+4k)+2−7k
-3+4k+2-7k
Add the numbers:
−3+4k+2−7k
−1+4k−7k
Add the same term to both sides of the equation:
−1+4k−7k
−1−3k
Graph -23 +y = 8.
y
8
9
8+
7+
6+
4+
3+
2+
1+
2
-9-8-7 -6 -5 -4 -3 -2.
1 2 3 4 5 6 7 8 9
-2+
-3+
-4+
-5+
-6t
-7+
Answers
Answer:
in the proprety of the number of negs and postive and y the graph -23+y=8 being that the nuber is -15
a. pattern:
b. recursive equation:
Answers
Answer:
Pattern
Step-by-step explanation:
It is a pattern because on X it goes down one. On Y it goes down 3.