Answers
Step-by-step explanation:
3:
h(x)=(-3x-15)/5
let y=(-3x-15)/5
interchanging role of x &y
x=(-3y-15)/5
5x+15=-3y
y=-(5x+15)/3
h-1(x)=-(5x+15)/3
not
equal to f(x)=(-3x-6)/4
Given function are not function of each other .
4:
g(x)=2/3x-2/3
let
y=2/3(x-1)
interchanging role of x &y
x=2/3(y-1)
3/2x+1=y
g-1(x)=3/2x+1
not equal to f(x)=½x+1
Given function are not function of each other .
Problem 1
Answer: You are correct. They are inverses--------------------
Explanation:
One way to see if we have an inverse pair or not is to compute these two composite functions
f(g(x))g(f(x))If both result in x, and just that, then we have shown that they are inverses of one another.
f(x) = (2x)/3
f(x) = (2/3)x
f(g(x)) = (2/3)*g(x)
f(g(x)) = (2/3)*(3/2)x
f(g(x)) = x
The steps to show that g(f(x)) = x are very similar
g(x) = (3/2)x
g(f(x)) = (3/2)*f(x)
g(f(x)) = (3/2)*(2/3)*x
g(f(x)) = x
So this verifies that you have the correct answer.
======================================================
Problem 2
Answer: These functions are inverses of each other.--------------------
Explanation:
We'll use the same idea as problem 1
f(x) = 2 - (3/4)*x
f(g(x)) = 2 - (3/4)*( g(x) )
f(g(x)) = 2 - (3/4)*( (-4/3)x + 8/3 )
f(g(x)) = 2 - (3/4)*(-4/3)x - (3/4)*(8/3)
f(g(x)) = 2 + x - 2
f(g(x)) = x
So far so good, but we need to check the other way around as well
g(x) = (-4/3)x + 8/3
g(f(x)) = (-4/3)*( f(x) ) + 8/3
g(f(x)) = (-4/3)*( 2 - (3/4)*x ) + 8/3
g(f(x)) = (-4/3)*(2) + (-4/3)*(-3/4)*x + 8/3
g(f(x)) = -8/3 + x + 8/3
g(f(x)) = x
This verifies that f(x) and g(x) are inverses of each other.
Problems 3 and 4 will have similar steps.
Related Questions
NEED HELP FROM SOMEONE SMART!!! A trapezoid's area can be calculated by the formula A = {(b + b2)h, where A stands for area, b, for the first base's length, b2 for the second base's length, and h for height. Find the area of the trapezoid below.
Answers
======================================================
Work Shown:
b1 = 14 and b2 = 6 are the two parallel bases
h = 9 is the height
A = area of trapezoid
A = h*(b1+b2)/2
A = 9*(14+6)/2
A = 9*20/2
A = 9*10
A = 90 square meters
A baker has 10 pies. He will cut all the ples into pieces that are each of the whole ple.
How many pieces of pie will there be?
Answers
Answer:
I believe it to be 80 pieces if they are all cut into 8 pieces
Step-by-step explanation:
Answer:
I'm not sure how big each of the pieces of the pie are but I'm guessing 20 if each piece of pie is 1/2. Good luck on the question. Sorry I couldn't help you much.
Step-by-step explanation:
What is the value of x???
Answers
Answer:
x=63
Step-by-step explanation:
The degree measure of a line is 180 degrees.
180 degrees is made up of 117 and x
117+x=180
x=63
What is the equation of a circle with center at (4, -2) and a radius of 7?
Answers
let h= 4, k=-2 and r= 7 then
(x-h)^2 + (y-k)^2 = r^2
(x-4)^2 + (y+2)^2 = 7^2
x^2 -8x +16 + y^2 +4y +4 = 49
x^2 +y^2 -8x +4y +16 +4-49 = 0
x^2 + y^2 -8x +4y -29 = 0 is the required eq
Can someone help me please
Answers
Answer:
4) 60 ft.²
5) 96 cm.²
6) 96
7) 126
8) 72
9) 32
10) 90
11) 216
(Formula for the area of a rectangle: length x width)
(Remember to follow PEMDAS when calculating the problems.)
The dot plots show the heights of boys and girls at a summer camp. Heights of Boys and Girls at Camp 2 dot plots with number lines going from 40 to 60. A plot is titled Boy's Heights. There are 0 dots above 40, 1 above 41, 3 above 44, 3 above 46, 2 above 48, 3 above 50, 4 above 52, 4 above 54, and 0 above 56, 58, and 60. A plot is titled Girl's Heights. There are 0 dots above 40 and 41, 2 dots above 44, 3 above 46, 1 above 48, 3 above 50, 4 above 52, 3 above 54, 4 above 56, and 0 above 58 and 60. Which is a true statement for most of the data in each plot? Most of the data in each plot are greater than 48. Most of the data in each plot are less than 48. Most of the data in each plot are around 52. Most of the data in each plot are around 54.
Answers
Answer:
A- most of the data in each plot is greater than 48
Step-by-step explanation:
took the test
Answer:
a
Step-by-step explanation:
a
given the degree of measure of angle KJH is 66 degrees find the measure in radians
Answers
9514 1404 393
Answer:
E) 0.366π
Step-by-step explanation:
There are π/180 radians in a degree.
66° = 66°(π/180°) = (66/180)π = 11/30π ≈ 0.366π radians
__
11/30 = 0.366... repeating, so would normally be rounded to 0.367
Suppose A and B are independent events. If P(A) = 0.6 and P(B) = 0.85, what is P(A and B)?
A. .34
B. .51
C. .17
D. .68
Answers
Answer:0.51 I just took the test
Step-by-step explanation:
suppos f(x) = x^3 find the graph of f(x+1)
Answers
Answer:
(x+)^3
Step-by-step explanation:
i need help with this math
Answers
Answer:
Perimeter = 56
Area = 196
Step-by-step explanation:
We use the Pythagorean theorem to calculate the half-length of the sides (a):
a² + a² = (7√2)²2a² = 7² * 22a² = 98a = 7Half of a side is 7, meaning that the full length is 14.
With that in mind we can calculate the perimeter and area:
Perimeter = 14 * 4 = 56Area = 14² = 196A translation is applied to the triangle formed by the points A (-1,4), B(-1,10), and C(3,6). The image is the triangle that has vertices. A’(3,4), B’(3,10), and C’(7,6).
The triangle was translated…
The answers:
4 units to then left
4 units up
4 units to the right
4 units down
Answers
The graphs below have the same shape. What is the equation of the blue
graph?
Answers
Answer:
Your answer is C
Step-by-step explanation:
You first look at what is in the parenthesis, and you do the opposite. In this case the opposite of one to the right is -1. Then you look on the outside of the equation. The graph when down three places, so -3
Maria sold 50 books, or
30% of her book collection,
at a garage sale. How many
books were in Maria's
collection?
No links please
Answers
Answer:
167 books.
Step-by-step explanation:
30% = 50 books
1% = 50/30
100% = (50/30) * 100
= 167 books.
What is the volume, in cubic cm, of a rectangular prism with a height of 10cm, a width of 20cm, and a length of 11cm?
Answers
Answer:
2200 cubic cm
Step-by-step explanation:
The volume of a rectangular prism is found using the formula:
V = l*w*h
V = 10 cm * 20 cm * 11 cm
V = 2200 cubic cm
Answer: 2200
Step-by-step explanation:
Two of the vertices of a triangle are located at (6,0) and (5,10) on the coordinate plane. The third vertex is located at (x,20) , where x is a negative value. The area of the triangle is 60 square units.
Using the shoelace formula (Green’s Theorem) in counterclockwise fashion, write an equation that can be used to find the value of x .
PLEASE I NEED HELP! ASAP I WOULD REALLY APPRECIATE IT!!
Answers
Using the shoelace formula (Green’s Theorem) in counterclockwise fashion, the value of x is -8.
What is Shoelace formula ?Area of Polygon can be calculated using Shoelace formula described by Mathematician and Physicist Carl Friedrich Gauss where polygon vertices are described by their Cartesian coordinates in the Cartesian plane.
A = [tex]\frac{1}{2} |x_{1} y_{2} +x_{2} y_{3}+........x_{n-1}y_{n} +x_{n} y_{1} -x_{2} y_{1} -x_{3} y_{2} - ........-x_{n}y_{n-1}-x_{2}y_{n} |[/tex]
Shoelace formula (Green’s Theorem)
A = [tex]\frac{1}{2} |x_{1} y_{2} +x_{2} y_{3}+........x_{n-1}y_{n} +x_{n} y_{1} -x_{2} y_{1} -x_{3} y_{2} - ........-x_{n}y_{n-1}-x_{2}y_{n} |[/tex]
Where A is the area of the polygon and n is the number of sides of the polygon.
Here A = 6, n = 3, [tex]x_{1}[/tex] = 6, [tex]y_{1}[/tex] = 0, [tex]x_{2}[/tex] = 5, [tex]y_{2}[/tex] = 10, [tex]x_{3}[/tex] = [tex]x[/tex], [tex]y_{3}[/tex] = 20
A = 60 = [tex]\frac{1}{2} |(6.10)+(5.20)+(x.0)-(5.0)-(x.0)-(6.20)|[/tex]
60 = [tex]\frac{1}{2} |60+100-10x-120|[/tex]
60 = [tex]\frac{1}{2} |40-10x|[/tex]
60 = [tex]|20-5x|[/tex]
So 20 - 5x = -60
5x = 80
x = 16
20 - 5x = 60
5x = -40
x = -8
since x is a negative value,
we can know x = -8
Hence the value of x is -8.
Find out more information about green's theorem here
brainly.com/question/27549150
#SPJ2
Can someone answer this please l
Answers
Answer:
Step-by-step explanation:
(5a + 18) + (48 - a) + (8a - 30) = 180 (Angles on a straight line)
5a + 18 + 48 - a + 8a - 30 = 180
12a + 36 = 180
12a = 180 - 36
a = 144/12
a = 12
therefore, the first angle is, 78 degree, second angle is 36 degree and third angle is 66 degree.
Therefore, the size of the smallest angle is 36 degree
144=12a
a=12
The middle angle= 36 degree
Give me brilliant
Evaluate the expression 18 - 5 + 4 / 5 x 1
Answers
Answer:
18 - 5 + 4 / 5 x 1
18-5+4/5
13+4/5
(75+4)/5
79/5
hope it is helpful to you
Help me out! I’ll give Brainly :) thank you!!
Answers
25-10
F(5)=15
Answer:
f(5) = 15
Step-by-step explanation:
To evaluate f(5) substitute x = 5 into f(x) , that is
f(5) = 5² - 2(5) = 25 - 10 = 15
Plz help me well mark brainliest if correct!!.....
Answers
Answer:
D
Step-by-step explanation:
Do I need to explain?
Answer:
D(8)
Step-by-step explanation:
So remember, 2 opposite sides of a triangle are equivelent.
We know that one of these sides are 3.
So the other side must be 3 as well.
This is 2 of the 4 sides of a rectangle.
If each side is 3, and there are two sides, this means that they add up to 6.
Subtract this from your total permiter:
22-6
=
16
Now remember, there are 2 sides left.
To find the answer, divide the 16(permiter left) by the 2(sides left):
16/2
=
8
This is your answer!
Hope this helps! :)
Select all the equations that are equivalent
Answers
Answer:
52=8n +4
4=52-8n
are equivalent
Answer:
a, b, c, e
Step-by-step explanation:
4(2n + 1) = 52 is the same as 52 = 8n + 4 if you use distributive property.
4 = 52 - 8n is the same as 52 = 8n + 4. The 8n is just subtracted from both sides.
4n = 48 is not the same as 4(2n + 1) = 52 or 52 = 8n + 4 or 4 = 52 - 8n.
n = 6 is the solution to the equation so it is equivalent.
PLEASE PLEASE PLEASE look below I am crying
Answers
Answer:
it's C
Step-by-step explanation:
Imagine a coordinate plane. Move 5 units away, you'll end up with (-5, 2).
Hope I helped
(−10x^2+9)+(8x^2 −5x+7)
Answers
Answer:
-2x^2-5x+16
Step-by-step explanation:
Remove parenthesis:
-10x^2+9+8x^2-5x+7
Combine like terms:
-10x^2+8x^2-5x+9+7
= -2x^2-5x+9+7
=-2x^2-5x+16
y are selling lollipops for $0.50 and candy bars for $1.50.
Lydia buys 6 lollipops and some candy bars.
If she spends $15 in total, how many candy bars, b, did Lydia buy?
Answers
Answer:
b=8
Step-by-step explanation:
You multiply $0.50 by 6 (to get the amount of money she spent on lollipops)=3 then you take the 3 and subtract it from $15 which gives you 12, finally you get 1.50-12 and do that 8 times which means she bought 8 candy bars
8. If AC = 2x + 2 and GF = 4x - 14, find the value of x.
help please??
Answers
Answer:
x=8
Step-by-step explanation:
2x+2 = 4x-14
16=2x
x=8
What is the Tan J? URGENT HELP PLS
Answers
Answer:
4th Option, [tex]\frac{12}{5}[/tex]
Hope this helps!
help pls!!!! would be appreciated thank you
Answers
Answer:
fairly sure its not the fourth one or the second one- so that narrows it down to the first and third one
Step-by-step explanation:
I have no idea how to solve this
Answers
Answer:
awww neither do i
Step-by-step explanation:
lol I got a 72 on my matb homework going to go jump off a cliff
WILL GIVE
BRAINLIST
...
.
Answers
Answer:
b. gain of 279 pounds
Step-by-step explanation:
107+85-27+114 = 279
Answer:
9100 + 107 + 85 - 27 + 114
Total weight = a. 9379 pounds
find the area of this parallelogram with the measurements 5.2cm and 8.4cm
Answers
Answer:
43cm square
Step-by-step explanation:
A= bh
A=8.4cm x 5.2cm
A=43.68cmsqr
Write an inequality for the graph
Answers
A closed circle means the inequality will be greater than (>) or less than (<)
An arrow pointing right to increasingly positive values means the inequality is getting greater (> or ≥)
A narrowing pointing left to increasingly negative values means the inequality is getting lesser (< or ≤)
So for this graph with an open circle and rightward pointing arrow, “x” will be some number on the number line greater than the first point of -38:
x > -38