Answers
Given:
The table of values for the function f(x).
To find:
The values [tex]f^{-1}(f(3.14))[/tex] and [tex]f(f(-7))[/tex].
Solution:
From the given table, it is clear that the function f(x) is defined as:
[tex]f(x)=\{(-14,11),(-7,-12),(-12,-5),(9,1),(10,-2),(-2,13)\}[/tex]
We know that if (a,b) is in the function f(x), then (b,a) must be in the function [tex]f^{-1}(x)[/tex]. So, the inverse function is defined as:
[tex]f^{-1}(x)=\{(11,-14),(-12,-7),(-5,-12),(1,9),(-2,10),(13,-2)\}[/tex]
And,
[tex]f^{-1}(f(a))=f^{1}(b)[/tex]
[tex]f^{-1}(f(a))=a[/tex] ...(i)
Using (i), we get
[tex]f^{-1}(f(3.14))=3.14[/tex]
Now,
[tex]f(f(-7))=f(-12)[/tex]
[tex]f(f(-7))=5[/tex]
Therefore, the required values are [tex]f^{-1}(f(3.14))=3.14[/tex] and [tex]f(f(-7))=5[/tex].
Related Questions
2 1/4 x 3 1/5 brainliest
Answers
Answer:
36/5
Step-by-step explanation:
9/4×16/5
144/20
36/5
hope this is helpful
Answer:
[tex]7\frac{1}{5}[/tex]
Step-by-step explanation:
1. start by turning the fractions improper fractions:
[tex]2\frac{1}{4} =\frac{9}{4}[/tex]
[tex]3\frac{1}{5} =\frac{16}{5}[/tex]
2. then multiply them together:
[tex]\frac{9}{4}[/tex] x [tex]\frac{16}{5}[/tex] = [tex]\frac{144}{20}[/tex]
3. then simplify the fraction:
[tex]\frac{144}{20}[/tex][tex]=\frac{36}{5}[/tex]
4. turn it into a proper fraction:
[tex]\frac{36}{5} =7\frac{1}{5}[/tex]
On the unit circle, which of the following angles has the terminal point
coordinates.
A. 45
B. 135
C. 225
D. 315
Answers
Answer: C. 225
Step-by-step explanation:
Heya Kitties!
What is the value of x?
18x−16=−12x−4
x =
Answers
Answer:
2/5
Step-by-step explanation:
18x+12x=-4+16
30x=12
x=2/5
Answer:
18x-16=-12x-4
18x+12x=-4+16
30x=12
x=12/30
x=2/5
If a bus travel for 120 minutes at a speed of 75 kilometers per hour how far has the bus traveled?
Answers
Answer:
150 km
Step-by-step explanation:
Put the minutes into hours 120min is 2 hours.
Distance = speed * time
Distance = 75 * 2
Distance = 150
Answer:
150 kilometers
Step-by-step explanation:
if the bus is going 75 kilometers an hour and they traveled for 120 minutes (exactly 2 hours) then you would just multiply 75 by 2 to get 150 kilometers total.
Hello, Brainly community!
This question is for all of those Calculus people out there.
The volume of a swimming pool is changing with respect to time, such that the volume is given by W(t), where W(t) is measured in cubic centimeters and t is measured in seconds. A tangent line is shown for W(t) at t = 3 seconds. Determine the best estimate for the value of the instantaneous rate of change of W(t) when t = 3.
(I've narrowed down the answer choices to 2, and just really need to find the right way of thinking to find the answer)
(A) W(lim t) as t goes to 3.
(B) [W(3.1) - W(2.9)] / 0.2.
Thank you in advance!
Answers
Answer:
(B) [tex]\displaystyle \frac{W(3.1) - W(2.9)}{0.2}[/tex]
General Formulas and Concepts:
Calculus
Limits
Derivatives
The definition of a derivative is the slope of the tangent line.Derivative Notation
Instantaneous Rates
Tangent Line: [tex]\displaystyle f'(x) = \frac{f(b) - f(a)}{b - a}[/tex]Step-by-step explanation:
Since we are trying to find a rate at which W(t) changes, we must find the derivative at t = 3.
We are given 2 close answer choices that would have the same numerical answer but different meanings:
(A) [tex]\displaystyle \lim_{t \to 3} W(t)[/tex](B) [tex]\displaystyle \frac{W(3.1) - W(2.9)}{0.2}[/tex]If we look at answer choice (A), we see that our units would simply just be volume. It would not have the units of a rate of change. Yes, it may be the closest numerically correct answer, but it does not tell us the rate at which the volume would be changing and it is not a derivative.
If we look at answer choice (B), we see that our units would be cm³/s, and that is most certainly a rate of change. Answer choice (B) is also a derivative at t = 3, and a derivative tells us what rate something is changing.
∴ Answer choice (B) will give us the best estimate for the value of the instantaneous rate of change of W(t) when t = 3.
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Book: College Calculus 10e
pls help me don't know what to do
Answers
Answer:
x=15
Step-by-step explanation:
The 60 degree angle and the (x+45) degree angle are both the same degree because they are vertical angles.
So to solve, just subtract 45 from 60
60-45=15
That's your answer!
Hope this helps!
How do u solve this ?
Answers
jordan wants to save to buy a car and decides to open a banking account that is offering an interest rate of 4.5% compounded annually how much will jordan have in the account after 5 years it he deposits $7,000 today?
Answers
Answer:
8,723.27$
Step-by-step explanation:
find the slope of the line passing through the points (-2,5) and (3/2,2)
Answers
Answer:
slope = - [tex]\frac{6}{7}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 2, 5) and (x₂, y₂ ) = ([tex]\frac{3}{2}[/tex], 2)
m = [tex]\frac{2-5}{\frac{3}{2}-(-2) }[/tex]
= [tex]\frac{-3}{\frac{3}{2}+2 }[/tex]
= [tex]\frac{-3}{\frac{7}{2} }[/tex]
= - 3 × [tex]\frac{2}{7}[/tex]
= - [tex]\frac{6}{7}[/tex]
Find the height h of the triangle.
Answers
Answer:
A, 12 times the square root of 3
Step-by-step explanation:
24 sqaured plus 12 squared=432
square root of 432=20.9
12 times the sqaure root of 3=20.9
The cost for 2 adults and 5 children to eat at the local buffet restaurant is \$46.50 . The cost for 1 adult and 1 child is $15. What is the cost of a child's meal ?
Answers
Answer:
c = 5.5
Step-by-step explanation:
2 a + 5 c = 46.50
a + c = 15
a = 15 - c
2(15-c ) +5c = 46.50
30 - 2c +5c = 46.5
3c = 16.5
c = 5.5
For the first equation there are 2 adults and 5 children so the equation is:-
2a + 5c = 46.50
And for the second equation there is 1 adult and 1 child. So the equation is:-
a + c = 15
a = 15 - c
You take this formula and substitute it to the above formula (2a + 5c = 46.50)
➡️ 2a + 5c = 46.50
➡️ 2(15 - c) + 5c = 46.50
➡️ 30 -2c + 5c = 46.50
➡️ 5c - 2c = 46.50 - 30
(You collect like terms)
➡️ 3c = 16.5
➡️ c = 16.5/3
➡️ c = 5.5
which describes the graph of y=-(x+5)^2+3
Answers
Answer:
Maximum at (-5, 3)
Step-by-step explanation:
The quadratic equation is in vertex form, which specifically shows the vertex.
Since the a is negative, you get a maximum y value of 3.
Vertex form: y=a(x-h)^2+k
Y’ = -2(x+5)
=> maximum when y’ = 0
help and explain//////////////////////////////////////////////
Answers
Answer:
(f + g)(x) = 5x - 3
Step-by-step explanation:
(f + g)(x)
= f(x) + g(x)
= 2x + 4 + 3x - 7 ← collect like terms
= 5x - 3
Answer:
5x - 3
Step-by-step explanation:
(f + g)(x) = f(x) + g(x)
= 2x + 4 + ( 3x - 7 )
= 5x - 3
Nathan is 1.55 meters tall. At 1 p.m., he measures the length of a tree's shadow to be 38.15 meters. He stands 32.9 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter .
Answers
Answer:
11.26 m
Step-by-step explanation:
The height of the tree is about 11.25 meters.
What are similar triangles?When the respective sides are proportional and the corresponding angles are congruent, two triangles are said to be similar.
Given that, the height of the person is 1.55 meters, the length of the tree's shadow is 38.15 meters, and the distance between the person and the tree is 32.9 meters.
Let the height of the tree be x.
Note that the scenario makes two similar triangles.
Since the ratio of the side lengths of similar triangles is proportional, it follows:
(38.15 - 32.9)/1.55 = 38.15/x
5.25/1.55 = 38.15/x
3.39 = 38.15/x
x = 38.15/3.39
x = 11.25
Hence, the height of the tree is about 11.25 meters.
Learn more about similar triangles: https://brainly.com/question/25882965
#SPJ2
What is the value of k?
Answers
Answer:
Step-by-step explanation:
recall that the inside angles of a triangle add up to 180°
and also that the angle 115° is the other part of a 180° total
180=115+y
180-115 =65
then the inside angle at Y is 65°
add the three inside (interior of the triangle) angles up
180= 65 + (4k+5) + (6k+10)
180 = 65 + 10k + 15
180 = 80 + 10k
100 = 10k
10 = k
see how I did that?
What type of health screening would this patient most likely receive?
Sue is a 45-year-old woman with a family history of breast cancer. Her healthcare professional will most likely recommend that she receive a .
Answers
Answer:
A mammogram is what she would receive
Step-by-step explanation:
Plot point C in GeoGebra to verify that it indeed lies on AB. You can enter the coordinates in the Input window to plot the point . Also , verify the distances you calculated in question 3 using GeoGebra . Take a screenshot showing the distances displayed by GeoGebra , and paste it below .
Answers
Answer:
The picture of file
Step-by-step explanation:
Your'e welcome
Helppp and explain pls and thankyou
Answers
Answer:
None of both
Step-by-step explanation:
It say y = lxl
so it mean if y = 3 so x = 3 or -3
A cinema is doing a promotion to celebrate their 50th anniversary for 1 week. They give
away a free drink to every 98th customer, a free bag of popcorn to every 112th customer and
a free cinema ticket to every 224th customer. Which lucky customer will be the first to
receive all 3 items?
Answers
Answer:
1,568 customer
Step-by-step explanation:
Find the lowest common multiple of 98, 112, and 224
98 = 98, 196, 294, 392, 490, 588, 686, 784, 882, 980, 1078, 1176, 1274, 1372, 1470, 1568, 1666
112 = 112, 224, 336, 448, 560, 672, 784, 896, 1008, 1120, 1232, 1344, 1456, 1568, 1680, 1792, 1904
224 = 224, 448, 672, 896, 1120, 1344, 1568, 1792, 2016, 2240
The lowest common multiple of 98, 112, and 224 is 1568
Therefore, the 1,568th customer will be the first to receive all 3 iitem
What is the value of x?
Answers
Answer:
D. 30°
Step-by-step explanation:
By exterior angle theorem:
x° + 70° = 100°
x° = 100° - 70°
x° = 30°
x = 30
At a certain store, a CD costs $12. If the cost of CDs were graphed as the output, compared to the number of
CDs purchased as input, which of the following would not be true of the graph?
A. The set of points would all lie on the same line.
B. The set of points would include the origin.
C. The set of points would rise from left to right.
D. The set of points would not graph a function.
Please select the best answer from the choices provided
A
B
C
D
Answers
Decrease £19064.67 by 9.5%
Give your answer rounded to 2 DP. (decimal place)
Please Help !!!
Answers
Answer:
17253.52
Step-by-step explanation:
100-9.5=90.5
19064.67*0.905=17253.52
5) On each birthday Rosa gets as many roses as she is old in years. She still has all the dried flowers and there are now 120 of them. How old is she? A) 10 B) 12 C) 14 D) 15 E) 20
Answers
Answer:
D) 15
Step-by-step explanation:
This is an arithmatic progression.
The formula for the sum of arithmatic progression is
[tex]s = \frac{n}{2} (2a + (n - 1)d)[/tex]
where d is the common difference between successive terms and a is the first term. By applying this formula,
[tex]120 = \frac{n}{2} (2(1) + (n - 1)(1)) \\ 120 = \frac{n}{2} (1 + n) \\ n(1 + n) = 240 \\ n {}^{2} + n - 240 = 0 \\ (n - 15)(n + 16) = 0 \\ n = 15 \: or \: n = - 16(reject)[/tex]
solve for x. Round to the nearest tenth, if necessary.
Answers
Answer:
7.1
Step-by-step explanation:
We used SOHCAHTOA because it's a right angle triangle
So because we have an angle with an adjacent of 6.3 and hypotenuse of x
We will use
Cos=adjacent /hypotenuse
Question
The quotient of a number and 5 has a result of 2. What is the number?
Answers
Answer:
10.
Step-by-step explanation:
Answer:
The number is 10.
Step-by-step explanation:
x/5 = 2
Multiply both sides by 5.
5 * x/5 = 5 * 2
x = 10
Answer: The number is 10.
Select the expression that represents the following statement: add 24 to the quotient of 16 and 8.
Answers
Answer:
16/8 + 24
Step-by-step explanation:
How is mathematical thinking established? How can we have mathematical thinking?
修改翻译结果
Answers
Translate How is mathematical thinking established? How can we have mathematical thinking? in to Chinese.
数学思维是如何建立的？ 怎样才能有数学思维？
According to the number line, what is the distance between points A and B?
0 6 units
7 units
O 12 units
O 14 units
Answers
Answer:
14 units
Step-by-step explanation:
A = - 2, B = 12
Therefore,
d(A, B) = 12 - (-2) = 12 + 2 = 14 units
2m^2-5m-3=0 by factorization
Answers
Answer:
M= 6, -1
Step-by-step explanation:
Factoring these numbers, it will result in (m-6)(m+1). So, m= 6,-1
find the domain of f(x)=sec(2x)
Answers
Answer:
*Refer the image attached
Step-by-step explanation:
*Refer the image attached
