Answer:
They are inverses since both composition equal x.
Step-by-step explanation:
Given the functions, f(x) = 3x + 1 and g(x) = (x-1) / 3, to check if they are inverses functions, we are to find the inverse of one of the function and check if it will give us the other function.
Let's look for the inverse of f(x).
Given f(x) = 3x+1
Let y = f(x) so that y = 3x+1
Replace y with x
x = 3y+1
Make y the subject of the formula of the resulting equation;
3y = x-1
y = (x-1)/3
The new function of x will be the inverse of f(x)
Hence f^-1(x) = (x-1)/3 = g(x)
Another way to check is to find their composition. Let's find f(g(x) and g(f(x)
F(g(x)) = f((x-1)/3)
Replace x with (x-1)/3 in f(x)
F(g(x)) = 3[(x-1)/3]+1
F(g(x)) = x-1+1
F(g(x)) = x
Similarly for g(f(x));
g(f(x)) = g(3x+1)
Replace x in g(x) with 3x+1
g(3x+1) = (3x+1-1)/3
g(3x+1) = 3x/3
g(3x+1) = x.
Since g(f(x)) = f(g(x)) = x, hence f(x) and g(x) are Inverses functions
A theater group made appearances in two cities. The hotel charge before tax in the second city was $1500 lower than in the first. The tax in the first city was
7.5%, and the tax in the second city was 7%. The total hotel tax paid for the two cities was $547.50. How much was the hotel charge in each city before tax?
Answer:
let the hotel charge before tax for second hotel be x
then the hotel charge before tax for first hotel = x+1500
tax of first hotel = 7.5% * (x+1500) = (7.5x+11250)/100
tax from second hotel= 7% of x = 7x/100
total tax = 547.50
7x/100 + (7.5x+11250)/100 =547.50
14.5x = 54750-11250
14.5x= 43500
x= 3000
hotel charge in first city = 4500
in second city =3000
Step-by-step explanation:
18. f-g4, if f =3 and g = -5=
Answer:
23
Step-by-step explanation:
Step 1:
3 - -5 (4)
Step 2:
3 - (-20)
Step 3:
3 + 20
Answer:
23
Hope This Helps :)
Randell's favorite brand of cookies is on sale at a price of $1.79 for a 12 ounces package. what is the cost per ounce (unit rate) for these cookies?
Answer:
$0.1492
Step-by-step explanation:
-17 = - 10 + x
Help me please
Answer:
x = -7
Step-by-step explanation:
Isolate x by adding 10 to both sides:
-17 = -10 + x
-7 = x
So, x = -7
Craig has acollection of 220 marbles. He lets his friend have 1/4 of his collection and sells 1/5 of his collection to the novelty store. He takes 15 marbles home to give to his brother. how many marbles remain in Craig's collection?
Answer:
he would have 106
Step-by-step explanation:
hope it helps
write a number where the digit 1 greater than the digit 7
1000-? i think that works
find the value of x. write your answer in simplest radical form
Answer:
[tex]x = 4 \sqrt{2} [/tex]Step-by-step explanation:
To find the value of x we can use either sine or cosine
Using cosine we have
[tex] \cos(\theta) = \frac{adjacent}{hypotenuse} [/tex]From the question
x is the hypotenuse
4 is the adjacent
We have
[tex] \cos45= \frac{4}{x} \\ x \cos45 = 4 \\ x = \frac{4}{ \cos(45) } [/tex]We have the final answer as
[tex]x = 4 \sqrt{2} [/tex]Hope this helps you
Step-by-step explanation:
Sinø=opp/hyp
Sin45=4/x. (× b.s by x)
xSin45=4. (÷ b.s by Sin 45)
x=4/Sin45
x=4.7
A footballer scores in one out of five matches. What percentage of the matches does the footballer score in?
Answer:
20%
Step-by-step explanation:
100 divided by 5 =20 20x1=20
Will give brainliest answer
Answer:
4 and 2 are the correct answers in that order
Can someone help me simplify 16 > x +9
Answer:
7 > x
Step-by-step explanation:
16 > x + 9
you subtract 9 from both sides to get your variable by yourself and you keep the same sign
7 > x
Given the points A(-5, -6) and B(8, 2), if C is the midpoint of segment AB, find the coordinates of the midpoint of segment CB
Please help me out !!!
Answer:
i cant see the exponent sorry
Step-by-step explanation:
ILL MARK BRAINLIST !!! SHOW WORK
Answer:
8748
Step-by-step explanation:
a^5b^-6
when replacing the variables with their values :
3^5 -6^2
3^5 = 3*3*3*3*3 = 243
(-6)^ 2 = 36
243 * 36 =
8748
what is the radius of 16\pi
The perimeter of a rectangle is 40 m. The length is 4 m more than three times the width. Find the length and the width of the rectangle.
Answer:
Width = 4 m, Length = 16 m
Step-by-step explanation:
Perimeter = 40
Width = x
Length = 3x + 4
x + x + 3x + 3x + 4 + 4 = 8x + 8
40 - 8 = 32
32/8 = x
x = 4
Width = 4
Length = 16
Please mark as Brainliest, thank you!
what is the answer to
5 1/6 times ( -2/5)
Answer:-31/15
Step-by-step explanation: step 1: make both fractions improper
step 2: multiply numerator and denominator 31/6 x -2/5= -62/30
step 3: simplify -31/15
27. Give the perimeter of the rectangle below in
simplest form.
Answer:
The permeter will be 26 units
Step-by-step explanation:
First to find this you need to know what the value of x is to do this I will use the equation 3x - 7 = x + 2
1. add seven to both sides leaving 3x = x + 9
2. Then subtract the 1x from both sides leaving 2x = 9
3. Then divide 9 by 2 which will be 4.5, x = 4.5
Then just plug 4.5 into each x value 4.5 + 2 and 3(4.5) - 7
1. 4.5 + 2 = 6.5
2. 3(4.5) - 7 13.5 - 7 = 6.5
The perimeter of the rectangle below in simplest form will be 4(x - 3).
Length of the rectangle = 3x - 7
Width of the rectangle = x+2
The perimeter of a rectangle is given as 2(length + width). The perimeter of the rectangle given will then be:
= 2(length + width)
= 2(3x - 7) + 2(x + 2)
= 6x - 14 + 2x + 4
= 4x - 12 = 4(x - 3)
Therefore, the perimeter of the rectangle in simplest form will be 4(x - 3).
Read related link on:
https://brainly.com/question/24429956
Find the value 10 4 exponent
Mr.Harris owns a bubble machine that he uses for different school events. The bubble solution contains 3/4 cup of corn starch for every 2 cups of water.
What is the rate in cups of corn starch pero cup of water
A.3/8
B.2/3
C. 1 1/2
D. 2 2/3
Answer:
3/8
Step-by-step explanation:
Divide 3/4 into 2. Got it right on iready
What is the coefficient of the x2 term of the algebraic expression 2x4 + x2 - x + 7
Step-by-step explanation:
2x⁴ + x² − x + 7
= 2x⁴ + 1x² + -1x + 7
The coefficient of the x² term is 1.
A jar contains 68 marbles, of which 26 are blue, 29 are red, and the rest are green. What is the ratio of green marbles to all marbles?
what is the square route of 36+2
square root 38
Step-by-step explanation:
imput square root 36 plus 2
What number is the opposite of 3.5
Answer:
-2/7
Step-by-step explanation: Thats the reciprocal so...
Bucky received $100 for his birthday. How many hours can he jet ski on Lake Smellsomemore if costs $15
per hour to rent a jet ski and he also has to spend $10 on an inflatable life jacket?
Answer:
b hours
Step-by-step explanation:
100 minus the 10 on the jacket equals 90. 90 divided by 15 is 6
Please help me with these two questions.
Answer:
gooooooooood
Step-by-step explanation:
I kie that
There are 6 black marbles, 14 blue marbles, 8 white marbles,
and 12 clear marbles in a bag. If Andy chooses a second marble
without replacing the first marble, what is P(black, then clear)?
Answer:
3/65 = 0.046 = 4.6%
Step-by-step explanation:
Notice that the total number of marbles is:
6 + 14 + 8 + 12 = 40
Then , the probability of getting a black marble first is 6/40 = 3/20
Now, since the experiment is without replacing, he is left with a total of 39 marbles in the bag, and the probability of getting a clear one is now 12/39
The total probability is the product of these two:
(3/20) x (12/39) = 3/65 = 0.046 = 4.6%
Jean masear is a saw operator in a lumber mill. He works 40 hours a week and earns $630 per week. What is his hourly pay rate
Answer:
[tex]\boxed {\tt \$15.75 \ per \ hour}[/tex]
Step-by-step explanation:
We want to find Jean's hourly pay rate. In other words, his pay per hour.
We can find the pay rate by dividing the money he is paid by the number of hours worked.
[tex]pay \ rate =\frac{money \ paid }{hours}[/tex]
He is paid $630 for 40 hours.
[tex]money \ paid= $630 \\hours= 40\ hours[/tex]
[tex]pay \ rate = \frac{\$630}{40\ hours}[/tex]
Divide.
[tex]pay\ rate = \$15.75 / hour[/tex]
His hourly pay rate is $15.75 per hour.
Order from greatest to least 1.202;1.29;1.02
Answer:
1.29, 1.202, 1.02
Step-by-step explanation:
calculate the M.A.D WILL BRAINLIST
Answer:
24/760/7Step-by-step explanation:
For the first dataset ...
d1 = {20, 22, 24, 28, 29, 29, 30}
The deviations from the mean of 26 are ...
d1 -mean(d1) = {-6, -4, -2, 2, 3, 3, 4}
so the total of the absolute values of these is 24. Since there are 7 numbers, the mean of the absolute deviations is ...
mad = 24/7
__
For the second dataset ...
d2 = {12, 15, 21, 30, 33, 35, 36}
The deviations from the mean of 26 are ...
d2 -mean(d2) = {-14, -11, -5, 4, 7, 9, 10}
so the total of the absolute values of these is 60. Again, there are 7 numbers, so the mean of the absolute deviations is ...
mad = 60/7
You are buying tickets to a Star Wars Convention. The tickets cost $10 per adult and $3 per child. Parking is a one-time fee of $5. If you
purchased two adult tickets, a, and the total cost was $109, how many child tickets, c, were purchased?
Answer:
28 children tickets
Step-by-step explanation:
$109 for the whole cost
bought 2 adult tickets that costed 10$ each and payed 5$ for parking fee
add them together 25$
109-25 =84
84/3 =28