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Explanation:
If g(x) is the inverse of f(x), and vice versa, then we have these two properties:
f(g(x)) = xg(f(x)) = xSince we want to find a function that is its own inverse, we want f(x) and g(x) to be the same function.
Through trial and error, you should find that f(x) = g(x) = x fit the description.
f(x) = x
f( g(x) ) = g(x) ... replace every x with g(x)
f( g(x) ) = x
You should find that g(f(x)) = x as well.
One possible answer is f(x) = x
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Through more trial and error, you should find that f(x) = g(x) = 1/x works as well. In fact, anything of the form f(x) = g(x) = k/x will work.
The proof can be written as follows
f(x) = k/x
f( g(x) ) = k/( g(x) )
f( g(x) ) = k/( k/x )
f( g(x) ) = (k/1) divide (k/x)
f( g(x) ) = (k/1) * (x/k)
f( g(x) ) = x
Through similar steps, you should find that g(f(x)) = x is the case also.
This proves that f(x) = k/x is its own inverse, where k is a real number constant.
Another possible answer is anything of the form f(x) = k/x
If we pick k = 3, then we get f(x) = 3/x which is the answer I wrote above.
You can pick any k value you want.
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There may be other types of functions that have this property, but I'm blanking on what they might be.
Helpppppppppp ASAP pls and thankyouu
Answer:
1. The graph of the inequality, y > -3·x - 2, created with MS Excel is attached showing the following characteristics;
Linear
Shade is above the line
2. The graph of the inequality, y ≤ │x│ - 3, created with MS Excel is attached showing the following characteristics
Linear
Shade is below the line
3. The graph of the inequality, y < x² - 4, created with MS Excel s attached showing the following characteristics;
Quadratic
Shade below the line
Step-by-step explanation:
Find the measure of the indicated aces and angles
Answer:
a=21
b=69
c=42
d=138
Step-by-step explanation:
c is supplementary to d (which is 138), so c=180-138= 42.
angle b is on the edge of the central angle 138, so b is 1/2, therefore, b=69.
angle a is complementary to angle b because any triangle that includes the diameter is a right angle, so angle a=90-69=21.
Given that is a standard normal random variable, find for each situation (to 2 decimals). a. The area to the left of is . (Enter negative value as negative number.) b. The area between and is . c. The area between and is . d. The area to the left of is . e. The area to the right of is . (Enter negative value as negative number.)
Answer:
-0.80
1.66
0.26
2.56
-0.50
Step-by-step explanation:
The values are the probability values either to the right or left of a given z - value ;
The Z - values could be obtained using the standard normal distribution table or a calculator :
Using the Z probability calculator ;
Area to the left of z is 0.2119
1.)
P(z < z) = 0.2119
z = - 0.8
2.)
Area between - z and z = 0.9030
Area to the left of z = 0.9030 plus
Area to the right of z = (1 - 0.9030) / 2 = 0.097/2 = 0.0485
(0.9030 + 0.0485) = 0.9515
P(z < z) = 0.9515
z = 1.66
3.)
Area between - z and z = 0.2052
Area to the left of z = 0.2052 plus
Area to the right of z = (1 - 0.2052) / 2 = 0.7948/2 = 0.3974
(0.2052 + 0.3974) = 0.6026
P(z < z) = 0.6026
z = 0.26
D.)
The area to the left of z is .9948
P(Z < z) = 0.9948
z = 2.562
E.)
The area to the right of z is .6915.
P(Z < z) = 1 - 0.6915
P(Z < z) = 0.3085
z = - 0.5
(3ab+2c)^3 what is the answer
Answer:
[tex]=27a^3b^3+54a^2b^2c+36abc^2+8c^3[/tex]
Step-by-step explanation:
[tex](3ab+2c)^3[/tex]
[tex]=(3ab+2c)[/tex] × [tex](3ab+2c)[/tex] ×
[tex]=(3ab+2c)(9a^2b^2+12abc+4c^2)[/tex]
[tex]=(3ab)(9a^2b^2)+(3ab)(12abc)+(3ab)(4c^2)+(2c)(9a^2b^2)+(2c)(12abc)+(2c)(4c^2)[/tex]
[tex]=27a^3b^3+36a^2b^2c+12abc^2+18a^2b^2c+24abc^2+8c^3[/tex]
[tex]=27a^3b^3+54a^2b^2c+36abc^2+8c^3[/tex]
hope this helps....
Can some help with this problem
I need help please, Model 3: Another plan to secure
Answer: Cant see the photo
Step-by-step explanation:
I cannot really see the photo
77/15 as a mixed number
Answer:
5 2/15
Step-by-step explanation:
Answer:
5 [tex]\frac{2}{15}[/tex]
Step-by-step explanation:
A mixed number consists of a whole number and a proper fraction (meaning the numerator is less than the denominator).
To get a mixed number, we are going to divide 77/15 using long division:
(I attached an image down below for you to understand better)
15 goes into 77 only 5 times with a remainder of 2.
So our whole number is 5
And the remainder of 2 become of the numerator of our proper fraction, with 15 being our denominator.
So your answer is 5 [tex]\frac{2}{15}[/tex]
Hope it helps (●'◡'●)
What are the coordinates of the point that 1/6 of the way from A to B
Answer:
D
Step-by-step explanation:
The distance from - 2 to 10 is 12. 12/6 is 2, so 2 spaces across
Find the measure of the missing angle using the exterior angle sum theorm.
Step-by-step explanation:
the correct answer for the question is 85
We know that, in a triangle,
Exterior angle = Sum of interior opposite angles
So,
missing angle = 45° + 40°
=> missing angle = 85°
ANSWER THIS PLEASE !!
Answer:
B. point B
Step-by-step explanation:
Answer:
B.
Step-by-step explanation:
B(-1, -3)
y = 3x
When x = -1,
y = 3(-1) = -3
Answer: B.
Pls help me with this set problem
(1) False. [tex]\{0\}\in\mathscr{U}[/tex] is saying "the set containing only 0 (that is, {0}) is an element of [tex]\mathscr U[/tex]", but this is not the case. [tex]\mathscr U[/tex] is the set containing only 0 and 1.
(2) True. [tex]\{0\}\subset\mathscr{U}[/tex] means "the set {0} is a subset of [tex]\mathscr{U}[/tex]". 0 itself is an element of [tex]\mathscr U[/tex], so {0} is indeed a subset of [tex]\mathscr U[/tex].
(3) True. 0 is clearly an element of [tex]\mathscr U[/tex].
(4) False. This statement says "0 is a subset of [tex]\mathscr U[/tex]" but 0 itself is not a set, it's a number.
Does anyone know how to solve these?
Answer:
1st graph: slope is -1 and equation is y=-x+5
2nd graph: slope is 2/5 and equation is y=2/5x-3
Step-by-step explanation:
y=mx+b is slope-intercept form.
It's call that because this forn tells us the slope,m, and the y-intercept,b.
The first graph you have identified b as 5 since you said the y-intercept was (0,5).
Now we just find slope by finding rise/run.
(0,5) is marked and we see another point has been marked, I will start at (0,5) go down 2 and right 2. This means rise=-2 and run=2 which means the slope=-2/2 and that reduces to -1.
The equation for first graph is y=-1x+5 or y=-x+5.
So again you have no problem identifying the y-intercept which is b=-3.
Now just count the rise/run to the other point. Starting at y-intercept we have to go up 2 and right 5 to get to the other point so m=2/5.
Which of the following graphs represents the equation y-2 = 3(x - 1)?
Answer:
Graph B
Step-by-step explanation:
The vertical intercept I am getting is (0,-1) and B is the only one with that point. Therefore, it should be B.
Solve the inequality.
k + 4 – 2(k – 12) > 0
k > 28
k > –20
k < –20
k < 28
k<28
Step 1: Simplify both sides of the inequality.
−k+28>0
Step 2: Subtract 28 from both sides.
−k+28−28>0−28
−k>−28
Step 3: Divide both sides by -1.
−k /−1 > −28 /−1
k<28
Answer:
k < 28
Step-by-step explanation:
Given inequality :-
k + 4 - 2( k - 12 ) > 0 k + 4 - 2k + 24 > 0-k + 28 > 0 28 > k k < 28Last Option is correct .
A rectangular floor of area 360 m2 is going to be tiled. Each tile is rectangular, and has an area of 240 cm2. An exact number of tiles can be put into the space. How many tiles will be needed??... Answer it
Answer:
1500
Step-by-step explanation:
The area of the regtangular floor is 360m². The floor is going to be retired with tiles having area of 240cm² . We need to find the number of times . Therefore ,
[tex]\implies 360m^2 = 360 \times 10^4 \ cm^2 [/tex]
And , the number of tiles required will be ,
[tex]\implies n =\dfrac{Area \ of \ floor}{Area \ of \ a \ tile }\\\\\implies n =\dfrac{ 360 \times 10^4 \ cm^2}{240 cm^2} \\\\\implies \underline{\underline{ n = 1,500 }}[/tex]
Hence the required answer is 1500 .
Which of these is the equation of the new function?
Question 2 of 10
If f(x) x/2-3 and g(x) = 4x^2 + x - 4, find (f + g)(x).
A. 4x+3x-7
B. 4x2+x-1
C. 66²-7
D. 4x + x-
Answer:
B
Step-by-step explanation:
Which of the following is an extranous solution
Answer:
x=2 is the answer
Step-by-step explanation:
find the positive square of 7.3441
Answer:
find the positive square root of 7.3441 Which of the following equations is equivalent to 6(3p – 2) = 20? 18p – 2 = 20 18p – 12 = 20 9p – 8 = 20 9p – 4 = 20 Three less than 3 times a number, n, is 19 more than twice the number.
Step-by-step explanation:
5 times 6 plus 1 times 8 plus 9 times 54 times 8 times 24 times 98 divided by 200 times 800 divided by 653 times 5782470
211512945555694/653
Decimal: 323909564403.819336
Instructions. Find the Area Of the square
Wrong answer Report
Right answer Heart
19.ans> Given,
Side = 9 m
To,find: Area
We,know that,area of the square is = (side)²
We,know that,area of the square is = (side)² = 9×9
We,know that,area of the square is = (side)² = 9×9 = 81 m
20.ans> Given,
Side= 7 cm
We,know that,area of the square is = (side)²
We,know that,area of the square is = (side)² = 7 × 7
= 49 cm
Hope it helps you ByeABCD is a quadrilateral.
a) Calculate the value of x.
b) When ABCD is drawn to scale, would the lines AD and BC be parallel or not? A You must justify your answer without using a scale drawing.
Answer:
A) 45=x
B) Yes, since both A and B are 90°
6x+90=360
6x=270
x=45
No lines are not parallel
if you are good at graphs this is good but please help it would mean a lot, I will give brain thingy
Answer:
(5, -6)
Step-by-step explanation:
The solution is where the lines cross.
Answer:
(5,-6)
Step-by-step explanation:
The solution to the system is where the two graphs intersect.
The graphs intersect at (5,-6)
Ling must spend no more than $40.00 on decorations for a party. She has spent $10.00 on streamers and wants to buy bags of balloons as well. Each bag of balloons costs $2.50. The inequality below represents x, the number of bags she can buy given the spending limit and how much she has already spent on streamers.
10 + 2.5 x less-than-or-equal-to 40
Which best describes the number of bags of balloons she can buy?
Answer:
she can buy 0 to 12 bags but no more
Step-by-step explanation:
Find the area of the parallelogram
Answer:
32
Step-by-step explanation:
8x4=32
Answer:need more time to solve-
Step-by-step explanation: A= b x h
Helpp m and explain ,I will mark brainlest:)
Answer:
(0,3) ; (2,3) ; (0,0) ; (3.5,0)
Step-by-step explanation:
Firstly, we have to plot all the giving inequalities as constraints
Not to forget, f(x) can be written as y
Kindly find the plot as an attachment
Upon plotting, we have the following vertices;
(0,3) ; (2,3) ; (0,0) ; (3.5,0)
Solve for xx. Round to the nearest tenth, if necessary.
Answer:
x ≈ 7.1
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos27° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{KL}{KM}[/tex] = [tex]\frac{6.3}{x}[/tex] ( multiply both sides by x )
x × cos27° = 6.3 ( divide both sides by cos27° )
x = [tex]\frac{6.3}{cos27}[/tex] ≈ 7.1 ( to the nearest tenth )
Which translation vectors could have been used for the pair of
figures?
Select each correct answer.
Find the difference of the polynomials given below and classify it in terms of degree and number of terms.
Answer:
4th degree polynomial with 4 terms
Step-by-step explanation:
Given:
3n²(n²+ 4n - 5) - (2n² - n⁴ + 3)
Open parenthesis
= 3n⁴ + 12n³ - 15n² - 2n² + n⁴ - 3
Collect like terms
= 3n⁴ + n⁴ + 12n³ - 15n² - 2n² - 3
= 4n⁴ + 12n³ - 17n² - 3
Number 1 term is 4n²
Number 2 term is 12n³
Number 3 term is -17n³
Number 4 term is -3
The highest degree of the polynomial is 4th degree
Therefore,
The difference in 3n²(n²+ 4n - 5) - (2n² - n⁴ + 3) is
4th degree polynomial with 4 terms
Answer:
4th degree polynomial with 4 terms
Step-by-step explanation:
line I is parallel to line m.if the maesure of angle 6 is 75 what is the measure of angle 3
Answer:
105
Step-by-step explanation:
l is parallel m so angle 3+angle 6=180
