Problem 1
Answer: False---------------------------------
Explanation:
The notation (f o g)(x) means f( g(x) ). Here g(x) is the inner function.
So,
f(x) = x+1
f( g(x) ) = g(x) + 1 .... replace every x with g(x)
f( g(x) ) = 6x+1 ... plug in g(x) = 6x
(f o g)(x) = 6x+1
Now let's flip things around
g(x) = 6x
g( f(x) ) = 6*( f(x) ) .... replace every x with f(x)
g( f(x) ) = 6(x+1) .... plug in f(x) = x+1
g( f(x) ) = 6x+6
(g o f)(x) = 6x+6
This shows that (f o g)(x) = (g o f)(x) is a false equation for the given f(x) and g(x) functions.
===============================================
Problem 2
Answer: True---------------------------------
Explanation:
Let's say that g(x) produced a number that wasn't in the domain of f(x). This would mean that f( g(x) ) would be undefined.
For example, let
f(x) = 1/(x+2)
g(x) = -2
The g(x) function will always produce the output -2 regardless of what the input x is. Feeding that -2 output into f(x) leads to 1/(x+2) = 1/(-2+2) = 1/0 which is undefined.
So it's important that the outputs of g(x) line up with the domain of f(x). Outputs of g(x) must be valid inputs of f(x).
The given statement is false.
What is composite function ?Composite function is a combination of two or more than two functions combined by mathematical operation of addition,subtraction,multiplication and division.Where output of one function is input to the other function.
According to the given question two functions are given f(x) and g(x) and and we have to compose in different order and see if they are same or not.
Given, f(x) = x + 1 and g(x) = 6x
So, (fog)(x) is, output of g(x) is the input of f(x) which is
f(6x) = (6x) + 1
f(6x) = 6x + 1.
Now, (gof)(x) is, output of f(x) is now input of g(x) which is
g(x+1) = 6(x+1)
g(x+1) = 6x + 6.
Thus we can see fog(x) ≠ gof(x).
learn more about composite functions here :
https://brainly.com/question/20379727
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Kristen has been waiting all summer for her family's annual road trip. This year, they're headed to Yellowstone National Park. Kristen just saw a sign that said the park is 10 miles away, so the drive is almost over. If Kristen's father drives 50 miles per hour, how many more minutes will it take to reach the park?
Answer: It will take 12 minutes to the reach the park.
Step-by-step explanation:
We know that, [tex]\text{Speed }=\dfrac{\text{distance}}{\text{time}}[/tex]
[tex]\Rightarrow\ \text{Time}=\dfrac{\text{Distance}}{ \text{Speed}}[/tex]
Given: Speed = 50 miles per hour
Distance needs to travel = 10 miles
Now, Time required to reach the park = [tex]\dfrac{10}{50}=\dfrac{1}{5}\text{ hour}[/tex]
Since 1 hour = 60 minutes
So, [tex]\dfrac15\text{ hour}=\dfrac15\times 60=12\text{ minutes}[/tex]
Hence, it will take 12 minutes to the reach the park.
6 2/9 ÷ (-2 2/3)
please help
- 2 1/3
Step-by-step explanation:Hi there !
6 2/9 : ( - 2 2/3) =
= (6*9+2)/9 : -(2*3+2)/3
= 56/9 : - 8/3
= 56/9 × - 3/8
simplify 56 - 8 ; 9 - 3
= 7/3 × - 1/1
= - 7/3
= - 2 1/3
Good luck !
What is the square of 9 is less than 100. True or false?
Square of 9 is 81 and it is less than 100
To show that the triangles are congruent, triangle ABC could be transformed by
which movement(s) to fit exactly on triangle XYZ?
Answer:
D a reflection over the x axis by a reflection over the y axis
Step-by-step explanation: if u put the triangle on the button left up then move it to the upper right it’s congruent.
Answer: A rotation of 270° clockwise about the origin followed by translation left 1 and up 10
Step-by-step explanation:
Does the expression x^3-1/x^2-1 simplify to x?
Answer:
no it doesn't
Step-by-step explanation:
[tex] \frac{ {x}^{3} - 1 }{ {x}^{2} - 1 } = \frac{(x - 1)( {x}^{2} + x + 1) }{(x - 1)(x + 1)} \\ [/tex]
( x - 1 )s simplifies
[tex] \frac{ {x}^{2} + x + 1 }{x + 1} \\ [/tex]
_________________________________
Thus ; the expression doesn't simplify to x.
2x + 5 = 8x-7-6x What is the answer to this question?
Answer:
No solution
Step-by-step explanation:
Jason bought a TV that was $1099.99. He made a
down payment of 199.99 and wants to pay the rest in
9 equal monthly payments. How much would he pay
each month?
What is the slope of the line shown in the graph?
1. 4/5
2. 5/7
3. 6/7
4. 5/6
The slope of the line is B. 5/7
A hot air balloon descends to the ground. The function a(t) = 210 – 15t can be used to describe the altitude of the balloon as it approaches the ground. The time is in minutes.
What does t represent?
What does a(t) represent?
What information will a(5.5) give?
Answer:
t represents the time in minutes since the balloon started descending.
a(t) represents the altitude of the balloon at t minutes.
a(5.5) gives the altitude at 5.5 minutes.
Answer:
What does t represent?
✔ time after the balloon begins to descend
What does a(t) represent?
✔ altitude of the balloon
What information will a(5.5) give?
✔ altitude of the balloon after 5.5 minutes
Step-by-step explanation:
edge 2021
plz make me brainliest
What is the length rounded to the nearest whole number? (length = 25.15 ft) *
Answer:
25
Step-by-step explanation:
Given B(17,5), C(11, -3), D-1, 2), and
E(x, -6), find the value of x so that BC || DE.
Answer:
[tex]x=-7[/tex]
Step-by-step explanation:
Remember that:
Two lines are parallel if their slopes are the same.Two lines are perpendicular if their slopes are negative reciprocals.And two lines are neither (a.k.a intersecting) if they are neither parallel nor perpendicular.We want to find the value of x such that [tex]\overline{BC}\parallel\overline{DE}[/tex].
Therefore, the slopes of BC and DE must be equivalent.
So, let's find the slope of BC first.
BC)
We can use the slope formula:
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Let B(17, 5) be (x₁, y₁) and let C(11, -3) be (x₂, y₂). Substitute:
[tex]\displaystyle m=\frac{-3-5}{11-17}[/tex]
Subtract:
[tex]m=-8/-6=4/3[/tex]
So, the slope of BC is 4/3.
DE)
Let D(-1, 2) be (x₁, y₁) and let E(x, -6) be (x, y₂). Substitute:
[tex]\displaystyle m=\frac{-6-2}{x-(-1)}[/tex]
We know that the two slopes must be equal. So, the slope of DE must also be 4/3. Substitute 4/3 for m:
[tex]\displaystyle \frac{4}{3}=\frac{-6-2}{x-(-1)}[/tex]
Solve for x. Simplify the right:
[tex]\displaystyle \frac{4}{3}=\frac{-8}{x+1}[/tex]
Cross multiply:
[tex]4(x+1)=-8(3)[/tex]
Multiply on the right:
[tex]4(x+1)=-24[/tex]
Divide both sides by 4:
[tex]x+1=-6[/tex]
Subtract 1 from both sides:
[tex]x=-7[/tex]
So, the value of x is -7.
And we're done!
pls help! see multiple choice. will give brainliest and 20 points
To adopt a dog from an animal shelter, you must pay $80 for vaccinations, $65 to spay or neuter the dog, and $50 for a wellness exam by a veterinarian.
a. Write an expression in simplest form that represents the amount (in dollars) it costs to adopt x dogs.
An expression is (?) dollars.
The equation with (x) in dogs and (y) in dollars is [tex]y=195x[/tex]
First, you must set up your equation.
[tex]y=80x+65x+50x[/tex]
Then, you must add like terms to simplify the equation
[tex]y=195x[/tex]
Answer:y=195x
Step-by-step explanation:
xd xd xd xd xd xd xd xd
Answer:
8576×7=60032
Step-by-step explanation:
Answer:
XDDDDDDDD
Step-by-step explanation:
1- Finding angle measures between intersecting lines
NOTE: Angles not necessarily drawn to scale
x = ??
Plz help!
Solve... 4x + 30 = -6(x - 2)
I got -4.2 but it's wrong!
Answer: x= -9/5 or x = -1.8
Step-by-step explanation:
4x + 30 = -6(x - 2) First apply the distributive property on the left side
4x + 30 = -6x + 12 Add 6x to both sides
+6x +6x
10x + 30 = 12 Subtract 30 from both sides
-30 -30
10x = -18 Divide both sides by 10
x = -9/5 or x = -1.8
Answer:
the answer is -1.8 if you want to use the decimal and -9/5 if you want to use the fraction
Step-by-step explanation:
4x + 30 = -6(x - 2)
4x+30 = -6x + 12
4x + 6x = 12 - 30
10x = -18
divide both side by 10
x = -9/5 or -1 4/5 or -1.8
( also not trying to gatekeep so i wanna say that i got this answer from an app named photomath. i scanned the question in the camera and it pulled the answer. hoped it helped love!)
i need help in finding the sum for (16 − x2) + (−14x2 + 7x5 − 17x4 + 9) plz help :( im rlly bad at math
Answer:
-50
Step-by-step explanation:
Please help with finding how many solutions a problem has.
Choose an equivalent expression for 123 • 129 • 124 • 122.
Answer:
Like what type of expression? And Is it for all the numbers at once, or is it each number separately?
Step-by-step explanation:
In a fruit salad, the ratio of watermelon to strawberries is 2:3. if there are 27 strawberries in the fruit salad, How many pieces of watermelon are there?
Answer: 18
Step-by-step explanation:
27 strawberries divided by 3 strawberries = 9
2 watermelon times 9 = 18 watermelon
help me pls u get 10 points
Which of the equations below will answer the following question? Select all that apply. Explain your answers.
I think of a number, add 7 and then multiply by 4. My answer is 80. What was my number?
x + 28 = 80
4(x+7) = 80
4x + 7 = 80
4x + 28 = 80
The graph represents the gallons of water in a water tank with respect to the number of hours since it was completely filled. The total capacity of the water tank is gallons, and the rate of change is gallons per hour.
Answer:
Total capacity of the water tank is 400 gallons
Rate of change in water level is 20 gallons per hour
Step-by-step explanation:
The graph attached represents the gallons of water in a water tank with respect to the number of hours since it was completely filled.
The total capacity of the water tank is represented by the y-intercept of the graph that is 400 gallons.
Now to calculate the rate of change in water level we will take two points on the given line and find the slope.
There are two points (0, 400) and (5, 300) on the line.
So the slope of the line is (400-300)/(0-5)= -100/5= -20
This minus notation of slope shows that level of water is reducing and rate of change in water level is 20 gallons per hour.
Please help me and explain the answer is the answer
Answer: C
Step-by-step explanation:
Pls help
Write a recursive AND explicit formula AND find the 7th term for each sequence:
1. 5,0,-5,-10
2. 3,4.5,6,7.5,9
Answer:
1)5-5x
2)3+1.5x
Step-by-step explanation:
5-5(7)=-30
3+1.5(7)=13.5
What is 8×∙(−7)∙3 = Because I need it right now for my HOMEWORK, so if you know the answer please tell me what it is.
Answer:
-168
Step-by-step explanation:
8 × -7 × 3
-56 × 3
-168
Is the line through points p (3,-5) and Q(1,4)parallel to the line through points R( -1,1) and S (3,-3)
Answer:
No
Step-by-step explanation:
To find out if the lines that go through the pairs of points are parallel, we must find the slope of each line. If the slopes are equivalent, then they are parallel. If not, then they are not parallel.
We can use the slope formula to find the slope between two points. The slope formula is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
where m is the slope between the points (x₁, y₁) and (x₂, y₂).
Lets first find the slope between points P and Q.
[tex]m=\frac{-5-4}{3-1}=\frac{-9}{2}=-4.5[/tex]
So the slope between P and Q is -4.5.
Now lets find the slope between the points R and S.
[tex]m=\frac{-3-1}{3-(-1)}=\frac{-4}{4}=-1[/tex]
So the slope between R and S is -1.
Since -4.5 does not equal -1, the lines are not parallel.
I hope you find my answer and explanation to be helpful. Happy studying.
x^2 - 7x = -4
solve by factoring
Step-by-step explanation:
x= -[tex]\sqrt{[/tex]7x - 4
Tamara wants to calculate the height of a tree outside her home. Using her clinometer, she measures the angle from 35 feet away from the base of the tree and gets an angle of 62°. Tamara's eye level is 5.5 feet above the ground. How tall is the tree?
Answer:
71.32 feet
Step-by-step explanation:
We set up a trigonometric function to get height of tree
Distance ,x = 35 feet away from tree base
Angle = 62⁰ at eye level
Y = tan(angle) * x
= Y = tan(62⁰) x 35
Y = 1.881 x 35
Y = 65.82 feet
We add Tamara's height to the total height of the tree
= 65.82feet + 5.5 feet
= 71.32 feet is the height of the tree
Someone help me please.