Answers
Answer:
f⁻¹(x) is not a function
Step-by-step explanation:
A function can only have one output value per input value. Multiple input values can have the same output value (horizontally), but multiple output values cannot have the same input value (vertically).
For example:
[tex]f(x)=x^2\\f(-2)=-2^2=4\\f(2)=2^2=4[/tex]
This function has 2 inputs with the same output. That is valid.
However, if you take the inverse of that function:
[tex]f^{-1}(x)=\sqrt{x}\\f^{-1}(2)=\sqrt{2}=1.414\\f^{-1}(-2)=\sqrt{-2}=\sqrt{2}i[/tex]
f⁻¹(-2) is an imaginary number. It doesn't exist, and so the inverse of f(x) is still a function because there is no vertical overlap. This is shown more clearly in the attached image.
The graph of the inverse of a function is just mirrored over y = x. This is also shown in the attached image. Any horizontal overlap the function may have becomes vertical overlap, and if those values still exist, the function cannot be a function.
In the function in your question, f(x) has some horizontal overlap around x = 0 and x = 8. If this was mirrored over y = x, the function at x = 8 would have 2 outputs, y = 0 and y = 8. As a result, it cannot be a function.
Let me know if I need to explain any part of that more clearly.
Related Questions
4. An archer shot a 0.12 kg arrow at a target. The arrow accelerated at 12,000 m/s to reach a speed of 50.0 m/s as it left the bow. During the acceleration, what was the net force on the arrow to the nearest newton?
Answers
Answer:
Step-by-step explanation:
ASSUMING you mean acceleration = 12000 m/s²
F = ma = 0.12(12000) = 1,440 N
There are multiples of 6 and 8
respectively listed below. Write
the least common multiple of 6
and 8 in the box.
factor
6, 8, 12, 16, 18, 24, 30, 32,36,40,42,48
Answers
Answer:
16
Step-by-step explanation:
if you skip count the 6×3 & 8×2 you will get 16
Answer:
The least common multiple is 16
What is the range of the function y= 2e7-1?
Answers
Answer:
The range of y = ex is all numbers greater than 0, so since the function has been shifted up 1, the new range of the function is all numbers greater than 1. Since the argument of any log must be greater than 0, (x-1)/2 > 0. Thus x - 1 > 0, so x > 1
Answer:
defines the set of values [ 1, 2, 3, 4, 5 ], and the range
1 : 3 : 5
defines the set of values [ 1, 4 ].
Although a range constant specifies a row vector, Octave does not normally convert range constants to vectors unless it is necessary to do so. This allows you to write a constant like 1 : 10000 without using 80,000 bytes of storage on a typical 32-bit workstation.
A common example of when it does become necessary to convert ranges into vectors occurs when they appear within a vector (i.e., inside square brackets). For instance, whereas
x = 0 : 0.1 : 1;
defines x to be a variable of type range and occupies 24 bytes of memory, the expression
15 is 25 % of what number?
Answers
Answer:
60
Step-by-step explanation:
What quadrant(s) is graph #5 in?
Answers
Answer:
Quadrant I: positive x and positive y.
Quadrant II: negative x and positive y.
Quadrant III: negative x and negative y.
Quadrant IV: positive x and negative y.
Step-by-step explanation:
Help Quick Please i beg
Answers
Answer:
Molly bought 6 erasers.
Step-by-step explanation:
It says Molly spent $18 on a magazine and some erasers. That means she only bought 1 eraser.
18 - 6 = 12.
12 / 2 =6.
Sketch the graph of each line y=-9x-5
Answers
I need help thanks very much
Answers
Answer:
154.92
Step-by-step explanation:
2014/13=154.92
PLEASE ILL GIVE BRAINLIEST! I NEED THIS ANSWER BY TODAY. NO LINKS AND DONT ANSWER IF YOU DONT KNOW!
Answers
Simplify: (2x - 5)/(x - 2) + (x - 8)/(x + 4) = f(x)
First, because you can't divide by zero,
note that x ≠ -4 or 2.
You have two fractions.
To add them you need a common denominator
8.
Write an equation in point-slope form for the line through the given point with the given slope.
(4, –6); m = 3/5
A. y - 6 = 3/5 (x+4)
B. y - 4 = 3/5 (x+6)
C. y + 6 = 3/5 x-4
D. y + 6 = 3/5 (x-4)
Answers
Answer:
D. y + 6 = 3/5 (x-4)
Step-by-step explanation:
Use the given slope and point to substitute into the point-slope formula y − y 1 = m ( x − x 1 ) .
Slope-intercept form: y = 3 /5 x − 42 /5
Point-slope form: y + 6 = 3 /5 ⋅ ( x − 4 )
The stem and leaf diagram shows the ages of people in a cinema.
2 1 3
Key: 2 1 represents 21 years
3 0 2 2 5
4 3 4 6 8 9 9
5 0 2 2 3 5
a) What is the range of ages? Iyears
b) How many people are represented in the diagram?
people
c) What is the median age?
years old
Answers
Answer:
A 34
B 17
C 47
Step-by-step explanation:
can anyone heelp me plzzzz
Answers
Answer:
1
Step-by-step explanation:
1 because we need to round down
Solve: 2 x + 5y + 5 = 0
2y=3x+17.
Find x and y
Answers
Answer:
x = -5 and y = 1
Step-by-step explanation:
a) 2x + 5y +5 = 0
a) 2x + 5y = -5
b) 2y = 3x + 17
b) y = 3/2x + 17/2
a) 2x + 5(3/2x + 17/2) = -5
a) 2x + 15/2x + 85/2) = -5
a) 19/2x = -5 - 85/2
a) 19/2x = -95/2
a) x = (-95/2) / (19/2)
x = -5
b) 2y = 3(-5) + 17
b) y = 2/2
y = 1
(1000÷1)×10-5000 Giving Brainliest
Answers
QUESTION TWO Determine whether or not a constant function can be
(a)one-to-one.
(b)an onto function. [10 marks]
Answers
=========================================================
Explanation:
The graph of any constant function is a horizontal flat line. The output is the same regardless of whatever input you select. Recall that a one-to-one function must pass the horizontal line test. Horizontal lines themselves fail this test. So this is sufficient to show we don't have a one-to-one function here.
Put another way: Let f(x) be a constant function. Let's say its output is 5. So f(x) = 5 no matter what you pick for x. We can then show that f(a) = f(b) = 5 where a,b are different values. This criteria is enough to show that f(x) is not one-to-one. A one-to-one function must have f(a) = f(b) lead directly to a = b. We cannot have a,b as different values.
----------------------------
The term "onto" in math, specifically when it concerns functions, refers to the idea of the entire range being accessible. If the range is the set of all real numbers, then we consider the function be onto. There's a bit more nuance, but this is the general idea.
With constant functions, we can only reach one output value (in that example above, it was the output 5). We fall very short of the goal of reaching all real numbers in the range. Therefore, this constant function and any constant function can never be onto.
Need the answer I’m lost
Answers
Answer:
A
Step-by-step explanation:
Tyler’s brother works in a shoe store.
Tyler’s brother earns a commission. He makes 4.5% of the amount he sells. Last week, he sold $500 worth of shoes. How much was his commission? $
The store bought a pair of shoes for $20, and sold it for $55. What percentage was the markup?
%
Tyler’s brother earns $16 per hour. The store offers him a raise—a 3% increase per hour. After the raise, how much will Tyler’s brother make per hour? $
Include the original amount and the raise when calculating your answer for this question.
answer as fast as you can cause i am in class!!!!!
Answers
Answer:
Step-by-step explanation:
4.5%/100 = 0.045
$500*0.045 = $22.5
A: Tyler makes $22.5 in commision
($55-$20)/$20*100 = 175% markup
100%+3%= 103%
$16*103% = $16.48
A: he would be making $16.48/hr
HEY. YES, YOU. PLEASE HELP
Answers
Answer:
it would be d
Step-by-step explanation:
yw
Find the value of x, then find EF.
X=
EF=
Answers
Hi I hope u have a great time ...
CD = FE
thus :
[tex]3x + 5 = 7x - 39[/tex]
Add both sides 39
[tex]3x + 5 + 39 = 7x - 39 + 39[/tex]
[tex]3x + 44 = 7x[/tex]
Subtract both sides 3x
[tex]3x - 3x + 44 = 7x - 3x[/tex]
[tex]44 = 4x[/tex]
Switch sides
[tex]4x = 44[/tex]
Divide both sides by 4
[tex] \frac{4x}{4} = \frac{44}{4} \\ [/tex]
[tex]x = 11[/tex]
There u go have a great day ♡
Every day you look out your window and see people walking dogs past your house with their dogs on a leash and a plastic bag in their hand. You conclude that all the people in your neighborhood are responsible dog-owners. What kind of reasoning is this?
Answers
Answer:
because they pick up there dog poop
Step-by-step explanation:
and they are good people
Which transformation from the graph of a function f of x describes the graphs of 10
Answers
Answer:
vertical stretch by factor of 10
Step-by-step explanation:
vertical stretch by factor of 10
At Ralphs 5 tomatoes cost $1.80.
At Vons 3 tomatoes cost $1.14.
Which is the better buy?
Answers
Answer:
I think 5 tomatoes cost $1.80
Answer:
Ralphs.
Step-by-step explanation:
Ralphs:
5 tomatoes = $1.80
1 tomato = $0.36
Vons:
3 tomatoes = $1.14
1 tomato = $0.38
Hence, Ralphs would be a better buy.
what is –5(–2) = i need help. will give brainlist
to corect awser.
Answers
Answer:
10
Step-by-step explanation: it'd be 10 because you're multiplying them and - by a - equals a positive!
[tex]-5(-2) = 10[/tex]
Compared to a model of 9/12 , a model of 3/4 will show -------------(A)3 Times as many B)1/3 times as many D)The same number of) parts that are each-----------(A)The same B)3 times the) size.
please help i need to get this done..;_;
Answers
9514 1404 393
Answer:
B, B
Step-by-step explanation:
A model of 9/12 will have 12 parts, 9 of which are shaded.
A model of 3/4 will have 4 parts (1/3 as many), 3 of which are shaded. Each part of this model will correspond to 3 parts of the 9/12 model. Hence, each part is 3 times the size of a part in the 9/12 model.
B) 1/3 times as many
B) 3 times the size
Solve for x.
1.
(3x)º
(8x)º
37°
Answers
Answer:
x=13
Step-by-step explanation:
3x+8x+37=180
11x+37=180
11x=180-37
11x=143
x=13
39,104and37
A tournament has 187 athletes. There are 91 more girls than boys. Let X represent the number of girls and let Y represent the number of boys. Write the system of equations that represents this situation
Answers
Answer: Need more info
Step-by-step explanation:
The system of equations that represents this situation will be;
⇒ 2Y + 91 = 187
What is linear expression?
A linear expression is an algebraic expression where each term is either a constant or a variable raised to the first power.
Given that;
Total athletes in a tournament = 187
And, In a tournament 91 more girls than the boys.
Now,
Let X represents the number of girls.
Let Y represents the number of boys.
Since, There are 91 more girls than the boys.
So, We can formulate;
X = 91 + Y
And, There are 187 athletes in a tournament.
So, We can formulate;
X + Y = 187
Substitute X = 91 + Y in above equation as;
91 + Y + Y = 187
91 + 2Y = 187
Thus, The system of equations that represents this situation will be;
⇒ 2Y + 91 = 187
Learn more about the system of equation visit:
https://brainly.com/question/28586904
#SPJ5
dani uses cotton balls to make snow men for an art project. dani has 14 cotton balls, and she uses 3 cotton balls to make each snow man.dani makes as many as she can.how many snowmen does dani make
Answers
Using the appropriate arithmetic operation, the number of snowmen Danny makes is 4
Total number of cotton balls = 14
Number of cotton balls per snowmen = 3
Creating a proportional relationship thus :
3 cotton = 1 snowman
14 cotton balls = x
Cross multiply
3x = 14
Divide both sides by 3
3x/3 = 14/3
x = 4.667
Hence, the number of snowmen that can be made is 4
Learn more : https://brainly.com/question/25644130
Answer:
4
Step-by-step explanation:
Arnie is an American teaching English in Japan, and he currently has 55,000
yen in his bank account. If the exchange rate changes from 1 U.S. dollar=
90.77 Japanese yen to 1 U.S. dollar = 91.24 Japanese yen, what happens to
the value in U.S. dollars of the money in Arnie's bank account?
Answers
Answer:
The worth of his bank account in USD would go from $605.93 to $602.81 cents. This is because it due to the change in exchange rates it requires more yen to make up a dollar which would cause it to take more yen to make a dollar. I hope this helps :D
The price of an item has been reduced by 35%. The original price was 85.
Answers
Answer:
$43.82
Step-by-step explanation:
100 / 85 = 1.176
1.176 x 35 = 41.18
85 - 41.18 = 43.82
Explanation: I just took the quiz!
what is the value of y?
Answers
Answer:
y = 10
Step-by-step explanation:
2y + 30 and 3y + 20 are known as vertical angles. They are equal to one another.
[tex]2y+30=3y+20\\\\2y+30-2y=3y+20-2y\\\\30=y+20\\\\30-20=y+20-20\\\\10=y[/tex]
