Use the functions f(x)=2x and g(x)= x^2+1 to find the value of each expression.
7. f(3)+g(4) 8. g(3)+f(4)
Answers
Answer:
First, you learned (back in grammar school) that you can add, subtract, multiply, and divide numbers. Then you learned that you can add, subtract, multiply, and divide polynomials. Now you will learn that you can also add, subtract, multiply, and divide functions. Performing these operations on functions is no more complicated than the notation itself. For instance, when they give you the formulas for two functions and tell you to find the sum, all they're telling you to do is add the two formulas. There's nothing more to this topic than that, other than perhaps some simplification of the expressions involved.
Step-by-step explanation:
To find the answers, all I have to do is apply the operations (plus, minus, times, and divide) that they tell me to, in the order that they tell me to.
(f + g)(x) = f (x) + g(x)
= [3x + 2] + [4 – 5x]
= 3x + 2 + 4 – 5x
= 3x – 5x + 2 + 4
= –2x + 6
(f – g)(x) = f (x) – g(x)
= [3x + 2] – [4 – 5x]
= 3x + 2 – 4 + 5x
= 3x + 5x + 2 – 4
= 8x – 2
(f × g)(x) = [f (x)][g(x)]
= (3x + 2)(4 – 5x)
= 12x + 8 – 15x2 – 10x
= –15x2 + 2x + 8
\left(\small{\dfrac{f}{g}}\right)(x) = \small{\dfrac{f(x)}{g(x)}}(
g
f
)(x)=
g(x)
f(x)
= \small{\dfrac{3x+2}{4-5x}}=
4−5x
3x+2
My answer is the neat listing of each of my results, clearly labelled as to which is which.
( f + g ) (x) = –2x + 6
( f – g ) (x) = 8x – 2
( f × g ) (x) = –15x2 + 2x + 8
\mathbf{\color{purple}{ \left(\small{\dfrac{\mathit{f}}{\mathit{g}}}\right)(\mathit{x}) = \small{\dfrac{3\mathit{x} + 2}{4 - 5\mathit{x}}} }}(
g
f
)(x)=
4−5x
3x+2
Related Questions
The distance between the paralled lines 3x + 4y +15 = 0 and 3x + 4y -10 = 0 is equal to: pls help ASAP
Answers
Answer:
5 units
Step-by-step explanation:
Please see attached pictures for the full solution.
(This distance is the perpendicular distance between the 2 parallel lines, which is the shortest distance between them.)
Answer:
D 21/5
Step-by-step explanation:
edge
5 -x -x = -1 what is x ?
Answers
Answer:
x=3
Step-by-step explanation:
[tex]5 - x - x = - 1 \\ 5 - 2x = - 1 \\ - 2x = - 1 - 5 \\ - 2x = - 6 \\ x = \frac{ - 6}{ - 2} \\ x = \frac{6}{2} \\ x = 3[/tex]
hope it helped you:)
Answer:
3
Step-by-step explanation:
5-2x=-1
-5__-5
____-6
-2
3
Nina’s total trip to and from work is 14 miles. If she works 243 days this year, how many miles will she drive to and from work?
Answers
Answer:
3,402
Step-by-step explanation:
Step 1:
243 × 14
Answer:
3,402
Hope This Helps :)
Answer:
3402
Step-by-step explanation:
Find the exact value of sin(140°)cos(20°) – cos(140°)sin(20°)
Answers
Given :
An expression sin(140°)cos(20°) – cos(140°)sin(20°) .
To Find :
The value of given expression .
Solution :
We know ,
sin(A - B) = sin A cos B - cos A sin B
By comparing with above formula , we get :
A = 140° and B = 20° .
So , sin(140°)cos(20°) – cos(140°)sin(20°) = sin ( 140°- 20°) = sin 120° .
Now , [tex]sin 120^\circ{} = \dfrac{\sqrt{3}}{2}[/tex]
Therefore , the value of expression is [tex]\dfrac{\sqrt{3}}{2}[/tex] .
Hence , this is the required solution .
The graph shows the number of miles traveled by a train over a 5 hour trip.
180
160
140
120
100
Miles
Traveled
80
60
40
20
0
1
2
4
5
3
Hours
How fast is the train traveling?
A. 30 miles per hour
B. 32.5 miles per hour
C. 35 miles per hour
D. 40 miles per hour
Answers
Answer: 35
Step-by-step explanation:
Plz helpp me!!?:) I don’t understand
Answers
-24 - (-13) = w
Simplify the left side
-24 + 13 = w
Add together like terms
-11 = w
Why is it imprecise to say that the equation 25 x 2 + 27 + 0 has no solution? Find all solutions of the equation.
Answers
Answer:
77
Step-by-step explanation:
77 is the only correct answer
Tom has 40$ to spend. He spend $21.40 on a light saber. He needs to set aside $15 for a toda t-shirt. If skittles cost $0.58 per package, what is the maximum number of skittles packages he can buy? PLEASE HELP
Answers
Answer:
6
Step-by-step explanation:
40 - 21.40 = 18.6
18.6 - 15, for the amount he sets aside for shirt = 3.6 left to spend
3.6 divided by 0.58 = 6.20
so rounded, the answer should be 6 packages of skittles
What is the range????????
Answers
How does a whale fall community affect ocean sediment? The decomposition of the whale enriches the sediment. The remains of the whale pollute the sediment. The sediment is transformed into food for mussels and crabs. The bacteria that are attracted break down the sediment nearby.
Answers
Answer:
The decomposition of the whale enriches the sediment.
Step-by-step explanation:
Answer:
The answer is A
Step-by-step explanation:
I just took the test and it was correct
hopefully this helps you :)
pls mark brainlest ;)
4d - p = m
Solve for d
Answers
Answer:
d=(m+p)/4
Step-by-step explanation:
The given equation solved for d as d=(m+p)/4.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation is 4d-p=m.
The given equation can be solved as
4d=m+p
Therefore, the given equation solved for d as d=(m+p)/4.
To learn more about an equation visit:
https://brainly.com/question/14686792.
#SPJ2
I am a multiple of 70. I am between 500 and 1000. My tens digit is odd. What number could I be?
Plz help also can you show the explanation too!
Answers
Answer:
Step-by-step explanation:
490 = 70 * 7
560 = 70 * 8
630 = 70 *9
700 = 70 * 10
770
840
910
You can fill in the other 3
So the number can be 630 770 or 910
Answer:
630, 770, 910
Step-by-step explanation:
They are multiples of 70 and the tens place number is odd 630, 770, 910
3.
Find a relationship between x and y so that (x, y) is equidistant from the two points (3,-1)
and (2,5). Show your work.
Answers
Answer:
The answer is 6.082763
Step-by-step explanation:
We use the Distance formula for this problem.
how many line of symmetry has a kite
Answers
Answer:
1
Step-by-step explanation:
Answer:
1
Step-by-step explanation:
Given b(x) = [X+41, what is b(-10)?
Answers
B(-10) = -10 + 41
B(-10) = 31 [Answer]
Translate into Algebra.
Jim will be x years old in two years. At that time, his sister will be twice as old as he will be. How old is Jim's sister now?
Answers
Let s be Jim's Sister's age now
s = 2x
X+1
If g(x) =
X-2 and h(x) = 4 - X, what is the value of (g•h)(-3)?
8/5
5/2
15/2
18/5
Answers
Answer: the correct answer is: 8/5
Step-by-step explanation: just took the quiz.
202·87–100·87–2·87=
Answers
Step-by-step explanation:
202·87–100·87–2·87
=99.13
Answer:
8700
Step-by-step explanation:
If you want it evaluated, this is the answer. 202 ·87-100·87-2·87= 17574-100·87-2·87=17574-8700-2·87=17574-8700-174= 8700
Similar triangles vs con congruent explanation
Answers
Answer:
Similar triangle means that only the angles are the same, but the sides are not. Congruent means the angles and sides are the same.
Represent the following sentence as an algebraic expression, where "a number" is the letter x. You do not need to simplify. The cube of the difference of 1 and a number.
Answers
Answer:
1-x=y cubed
Step-by-step explanation:
difference between 1 and a number is 1-x and the answer to this you cube.
In February 2009, the Harris Poll asked a sample of Americans whether they thought churches and religious groups have too much or too little power and influence on Washington†. The opinions of Americans were 34% too much, 57% too little, 4% just right, and 5% unsure.
Answers
Complete question is;
In February 2009, the Harris Poll asked a sample of Americans whether they thought churches and religious groups have too much or too little power and influence on Washington†. The opinions of Americans were 34% too much, 57% too little, 4% just right, and 5% unsure. (a) What type of distribution is this? cumulative frequency distribution simple frequency distribution cumulative percent distribution relative percent distribution (b) Knowing that 1,010 adults were polled nationwide, how many Americans polled felt that churches and religious groups have too little power and influence on Washington? (Round your answer to the nearest whole number.) Americans
Answer:
A) Relative percent distribution
B) 576 Americans
Step-by-step explanation:
A) We are given that the opinions of Americans were 34% too much, 57% too little, 4% just right, and 5% unsure.
This means that number of people in each of this category was divided by total number of people in the poll and multiplied by 100%.
Thus,it is relative percent distribution.
B) Since 1,010 adults were polled nationwide, therefore the number of Americans polled felt that churches and religious groups have too little power and influence on Washington = 57/100 × 1010 ≈ 576 people
Solve: −6x+4≤−16−2x . Express your answer in interval notation. (Express your answer in interval notation. Use U to indicate a union of intervals, and "oo" to express ∞)
Answers
Answer:
[5, oo)
Step-by-step explanation:
Add 6x+16 to both sides:
20 ≤ 4x
5 ≤ x . . . . . . divide by 4
The solution interval is [5, oo).
Answer:
A is the answer
Step-by-step explanation:
?show that 33105 is divisible by 15?
Answers
Answer:
um 2207 times 15 is 33105
Solve for the following variable.
Answers
Answer:
answers in the explanation.
Step-by-step explanation:
1. x=12
2 x=7
3.x=8
4.x=5
Write The slope intercept Form of the equation of a line with a slope of -4 that passes through the point (4,4)
Answers
Answer: y = 4x - 12
Step-by-step explanation:
4. So
3. Gecko Wireless has a 1000 minute monthly plan
that costs $29.95. Each bill also includes $2.95 for
federal communications tax and $0.05 per minute
over 1000. If m represent the minutes over 1000,
which equation represents the cost, p, of wireless
phone service? (MAFS.912.A-CED. 1.1)
defin
solut
a. P= 29.95 + 2.95
b. P=0.05 + m(29.95 +2.95)
P= 29.95 + 0.05m +2.95
d. P= (29.95 + 0.05)m +2.95. What equation should I use?
Answers
Answer:
[tex]P=29.95+0.05m+2.95[/tex]
Step-by-step explanation:
The monthly plan costs starts at $29.95, so we're not changing that.
For each monthly plan, we have to pay a tax of $2.95, so we're not changing that.
If we go over 1,000 minutes, we have to pay $0.05 for every minute we go over, and with the fact that [tex]m[/tex] represents each minute over 1,000, we're going to have to represent minutes over 1,000 as [tex]0.05m[/tex] in our equation.
Set up your equation:
[tex]P=29.95+0.05m+2.95[/tex]
Given the replacement set {0, 1, 2, 3, 4}, solve 6x – 3 = 3.
Answers
Answer: The answer is 1
It is 1
Step-by-step explanation:
A point lies on AB and is 1/4 the distance from A to B. Point A is located at (2, 8) and point B is located at (8, 5).
What are the coordinates of this point?
Answers
Answer:
[tex](\frac{7}{2} ,\frac{29}{4} )[/tex]
Step-by-step explanation:
I’ll mark you brainliest for the first response! Explain answer in full detail.
Answers
Answer:
x = 25
Step-by-step explanation:
2x + 4 + x + 11 = 90, combine like terms
3x + 15 = 90, subtract 15 from both sides
3x = 75, divide by 3
x = 25, you have your answer!
Which inequality is true? Use the number line to help.
A number line going from negative 5 to positive 3 in increments of 1.
1.5 greater-than 2 and one-half
One-half greater-than 0.5
Negative 2.5 greater-than negative 1.5
Negative 3 and one-half greater-than negative 4.5
HELP ME
Answers
Answer:
c
Step-by-step explanation:
i did the assignment on E2020
Answer:
c
Step-by-step explanation: