Answers
Answer:
g(f(x)) = x
Yes, the functions are inverses.
Step-by-step explanation:
Hi there!
We're given:
[tex]f(x) = 8x-7[/tex]
[tex]g(x)=\displaystyle\frac{x+7}{8}[/tex]
To solve for g(f(x)), plug f(x) into g(x) as x:
[tex]g(f(x))=\displaystyle\frac{(8x-7)+7}{8}\\\\g(f(x))=\displaystyle\frac{8x-7+7}{8}\\\\g(f(x))=\displaystyle\frac{8x}{8}\\\\g(f(x))=x[/tex]
Because g(f(x)) = x, the two functions are inverses.
I hope this helps!
Related Questions
find tge equation of the line
Answers
Answer:
y = -2x + 9 or y = 9 - 2x
Step-by-step explanation:
First find the gradient
Pick two points on the graph, (4, 1) and (1,7)Find the change in y (7 - 1 = 6)Find the change in x (1 - 4 = -3)Divide the change in y by the change in x = 6 ÷ -3 = -2The gradient is -2: y = -2x + cNext, look at where the line intercepts (goes through) the y-axis: 9
The equation of the line is y = -2x + 9
Tip: The gradient is negative because the line is going downwards from left to right; if the line was going upwards, the gradient would be positive.
Hope this helps!
Equivalent (-1)+10+9 please
Answers
Answer:
18
Step-by-step explanation:
1) Simplify the expression
-1 + 10 + 9
9 + 9
18
write an inequality whose solutions are represented by the shaded part of the graph
Answers
Answer:
x > 3
Step-by-step explanation:
PLEASE HELP!!
(04.03)
Given the function g(x) = 5(2)^x, compare the average rate of change from x = 1 to x = 2 and from x = 3 to x = 4.
How many times greater is the average rate of change from x=3 to x=4 than from x=1 to x=2?
О 4 times
O 5 times
O 2 times
O The average rate of change of Section B is not greater than the average rate of change of Section A.
Answers
Answer: Choice A. 4 times
========================================================
Explanation:
We'll be using this formula
[tex]m = \frac{f(b)-f(a)}{b-a}[/tex]
to compute the average rate of change (AROC) from x = a to x = b. Note how this is effectively the slope formula because y = f(x).
To start things off, we'll compute the AROC from x = 1 to x = 2.
[tex]m = \frac{g(b)-g(a)}{b-a}\\\\m = \frac{g(2)-g(1)}{2-1}\\\\m = \frac{5(2)^2-5(2)^1}{2-1}\\\\m = \frac{10}{1}\\\\m = 10\\\\[/tex]
Do the same for the AROC from x = 3 to x = 4.
[tex]m = \frac{g(b)-g(a)}{b-a}\\\\m = \frac{g(4)-g(3)}{4-3}\\\\m = \frac{5(2)^4-5(2)^3}{4-3}\\\\m = \frac{40}{1}\\\\m = 40\\\\[/tex]
The jump from m = 10 to m = 40 is "times 4", which is why choice A is the final answer.
help its due in 3 mins
Answers
Answer:
Can you please give me the question or link
Step-by-step explanation:
(3)
(2)
2 m
5 m
2 m
5 m
Perimeter:
Area:
Answers
Step-by-step explanation:
The area = (5 × 3) + (2 × 3) = 15 + 6 = 21
The perimeter = 2 + 3 + 5 + 5 + 3 + 2 = 20
please give me a brainliest answer
George is looking at stock market charts. He can buy a collection of stocks for 6 shares for $618. How much would it be for 11 shares?
Answers
Which expression is equivalent to 6m + (m – 2)(m + 7) + 3?
Answers
Answer:
m^2+11m-11.
Step-by-step explanation:
Answer: When x=10 , both expressions have a value of 33. James determined that these two expressions were equivalent expressions using the values of x= 4 and x=6 .Which statements are true? Check all that apply. When x=2, both expressions have a value of 18. The expressions have equivalent values for any value of x.
Step-by-step explanation:
Hope this helps!
what is the equivalent value of 1/3×(−15)
Answers
Answer: -5x
Find h. h - 6 = 5
(A) 5
(B) -1
(C)11 (D)6
Answers
h-6=5
first add 6 to both sides and you’ll get h=11
Answer:
C
Step-by-step explanation:
pls help!!! i will give brainliest!!!!! :D
Answers
Answer:
31 cm
Step-by-step explanation:
the scatterplot is rising, so based on an assumption of where a line going through the scatterplot is going to go, you get 41
The inequality 2x+1>15 will be true when
1. x=7
2. x=0
3. x=10
4. x=5
Answers
Answer:
3.) x = 10
Step-by-step explanation:
Let’s plug it into our equation
2(10) + 1 = 21
21 is greater than 15
Which statement correctly compares the function shown on this graph with
the function y = 4x + 2?
8
7
6
5
1
543 2
1 2 3 4
5
A. The function shown on the graph has a greater rate of change, but
a lower starting point.
B. The function shown on the graph has a greater rate of change and
a higher starting point.
C. The function shown on the graph has a smaller rate of change, but
a higher starting point.
Answers
The given highest power of x in the given function, y = 4·x + 2, is 1,
therefore, the graph of the function is a straight line.
The statement that correctly compares the function shown on the graph
with the function; y = 4·x + 2 is; C. The function shown on the graph has a
smaller rate of change but a higher starting point.
Reasons:
The given function is; y = 4·x + 2
Comparing with the equation for a straight line; y = m·x + c, we have;
The rate of change or slope, m = 4
The y-intercept, starting point, c = 2
Two points on the function shown on the graph are; (0, 4), and (-2, -2)
The slope of the given graph is therefore;
[tex]m = \dfrac{4 - (-2)}{0 - (-2) } = \dfrac{6}{2} = 3[/tex]
The rate of change of the graph, m = 3
The equation of the graph is therefore;
y - 4 = 3·(x - 0)
Which gives;
y = 3·x + 4
The y-intercept, starting point of the graph, is therefore, c = 4
Which gives;
The function shown on the graph has a higher starting point but a smaller rate of change than the given function.
Learn more here:
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A shipment of sugar fills 2 4/5 containers. If each container holds 2 3/7 tons of sugar, what is the amount of sugar in the entire shipment?
Write your answer as a mixed number in simplest form.
Answers
Answer:
6 4/5 tonsStep-by-step explanation:
Multiply the number of containers by the amount in each to find the total amount of sugar:
2 4/5 * 2 3/7 = 14/5 * 17/7 = 2*17/5 =34/5 = 6 4/5pls pls pls help meeee!
Answers
Answer:
x is 90 because it is a right triangle
Can someone help me plz!!
Answers
Answer:
MRT or TRM
Step-by-step explanation:
RT and MR meet at point R. Point R must be included in the final angle as well as the endpoints of RT and MR. The resulting angle is thus MRT, or TRM
A number n decreased by 8 is 19
Answers
Answer:
n-8=19
Step-by-step explanation:
The temperature dropped 4°C every hour for 6 hours. What was the total number of degrees the temperature changed in the 6 hours?
Answers
Answer:
-24 degrees Celsius
Step-by-step explanation:
6 x -4 = -24
Answer:
24 degrees.
Step-by-step explanation:
6 * 4 = 24.
Pls help me !!!!!! With question number one
1. Angelica is five years less than double Jaheim’s age . Jaheim is 14years old . How many years old is Angelica
Answers
Answer:
23
Step-by-step explanation:
14x2=28-5=23
Answer:
23
Step-by-step explanation:
add 14+14= 28-5=23
I need help with this problem
Answers
The room is 12 by 14
And walls are 8ft tall
There are two walls that have the dimensions of 12(8) and two that have the dimensions of 8(14).
The final equation would be…
2(96) + 2(112)
Simplify
192 + 224 = 416
(-0.4)^2 sum pls i need this by tonight i have to finish my math corrections pls
Answers
Answer:
(-0.4)²
= -0.4×-0.4
product of two negative numbers is positive
so, 0.4×0.4
=4/10×4/10
=16/100
=0.16
Given:
∠
A
E
D
≅
∠
A
C
B
.
∠AED≅∠ACB.
Prove:
∠
A
B
C
≅
∠
A
D
E
∠ABC≅∠ADE.
Answers
The triangles have a common vertex angle, and a given pair of
corresponding and congruent angles, they are therefore similar triangles.
∠ABC ≅ ∠ADE (CASTC)Reasons:
The given parameters are;
∠AED ≅ ∠ACB
By observation, we have that ΔAED and ΔACB have ∠A = ∠DAE and ∠A =
∠BAC in common.
Therefore, ∠DAE ≅ ∠BAC, by reflexive property.
Two angles of ΔAED (∠AED and ∠DAE) are congruent to two angles in
ΔACB.
(∠ACB and ∠BAC), which gives that ΔAED and ΔACB are similar by AA
Angle-Angle similarity postulate, and by Corresponding Angles of Similar
Triangles are Congruent CASTC we have;
∠AED ≅ ∠ACB
∠DAE ≅ ∠BAC
∠ABC ≅ ∠ADELearn more here:
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What is the slope of this line?
Enter your answer as a whole number or a fraction in simplest form.
Answers
y=2
Explanation:
Just trust me
if you take 3 apples from 10 apples how many do you have
Answers
Answer:
7
Step-by-step explanation:
Answer:
You will have exact seven.
The length of a side of a square is given by the expression 2x + 1, and its perimeter is 56.
[I have the equation, 4(2x + 1) = 56 down but I want to make sure that x actually equals 6.5]
Answers
Answer:
Step-by-step explanation:in the picture
Answer:x=[tex]\frac{13}{2}[/tex] or x= 6.5 either way x equals to the number 6.5 .
Step-by-step explanation:The image below will explain how you solve the problem also thanks for the person above me for the idea of answering this question.
HOPE THIS HELPS
:)
Also website as seen in the photo is symbolab
I need help asap please
Answers
Answer:
[tex]p(t) = - 3t + 75 \\ p(t) = 0 \\ - 3t + 75 = 0 \\ 3t = 75 \\ t = \frac{75}{3} \rightarrow \boxed{t = 25 \: mins} \\ 3 \: papers \: per \: mins \\ domain \: \boxed{t \geqslant 0} \: \\ because \: time \: cant \: be \: negative \: on \\ \: this \: perticular \: occasion \\ \therefore \: range \: \boxed {p(t) \geqslant 0 }[/tex]
on a shopping trip, Gina buys two books priced $4.99 and $12.99. She also buys 2 notebooks, 2 packs of pencils, and 3 composition books. The books are on sale for 10% off the list price and school supplies are 15% off. The store charges 6.5% sales tax. Item Cost ($) Notebooks 2.88 Composition Books 0.79 Pencil Packs 1.89
Answers
The total cost of items Gina bought on her shopping trip given the percentage discount is $26.31
Given:
cost of two books = $4.99 + $12.99
= $17.98
Amount paid for books = $17.98 - 10% of $17.98
= 17.98 - 0.1 × 17.98
= 17.98 - 1.798
= $16.182
Cost of notebooks = quantity × price
= 2 × $2.88
= $5.76
cost of composition books = quantity × price
= 3 × $0.79
= $2.37
cost of pencil packs = quantity × price
= 2 × $1.89
= $3.78
Total cost = $5.76 + $2.37 + $3.78
= $11.91
Amount paid for school supplies = $11.91 - 15% of $11.91
= 11.91 - 0.15 × 11.91
= 11.91 - 1.7865
= $10.1235
Therefore,
total cost of all items Gina bought = $16.182 + $10.1235
= $26.3055
Approximately, $26.31
Read more:
https://brainly.com/question/19535437
On a map, 1 inch equals 15 miles. Two cities are 7 inches apart on the map. What is the actual
distance between the cities?
The actual distance between the cities is miles.
Answers
Answer:
105 miles
Step-by-step explanation:
The ratio you have is 1:15
So you must multiply 7 by 15 to find the actual distance in miles.
7*15=105
3. A person jogs 1/7 mile in 1/42 hour. What is the person”s speed in miles perhour?
Answers
Answer:
42/7 = 6 miles per hour
Step-by-step explanation:
Given,
The total distance covered by the person = [tex]1/7[/tex] a miles,
Time taken by him = [tex]1/42\\[/tex]an hour,
We know that, speed = Distance, time
The speed of the person = [tex]1/7 over 1/42[/tex]
42/7
also known as 6 miles per hour
I hope this helps and have a great day!
Find the slope of the line that passes through (-68, 47) and (-66, 33).
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Quick please
Answers
Answer:
- 7Step-by-step explanation:
The slope formula:
[tex]m=(y_2-y_1)/(x_2-x_1)[/tex]Substitute the values to get:
[tex]m=(33-47)/(-66+68)=-14/2=-7[/tex]_________
[tex] \: [/tex]
(X1, X2) = (-68, 47)
(Y2, Y1) = (-66, 33)
Soo :
m = [tex]\frac{Y2 - Y1}{X2 - X1}[/tex]
m = [tex]\frac{33 - 47}{68 - 66}[/tex]
m = [tex]\frac{-14}{2}[/tex]
m = [tex]\boxed{\bold{-7}}[/tex]
Done.