The one-to-one functions given as sets of points and their possible inverse functions are given as
h = { (1,1), (2,2), (3,3), (4,4), (5,5), (6,6)}
g = { (1,3), (2,6), (3,9), (4,12), (5,15), (6,18)}
f = { (1,2), (2,3), (3,4), (4,5), (5,6), (6,7)}
i = { (1,1), (2,3), (3,5), (4,7), (5,9), (6,11)}
h⁻¹ = { (1,1), (2,2), (3,3), (4,4), (5,5), (6,6)}
i⁻¹ = { (1,1), (3,2), (5,3), (7,4), (9,5), (11,6)}
g⁻¹ = {(3,1), (6,2), (9,3), (12,4), (15,5), (18,6)}
f⁻¹ = {(2,1), (3,2), (4,3), (5,4), (6,5), (7,6)}
The inverse function of a given function should have the coordinates reversed.
Therefore the matches between the given functions and their inverse functions are given in the table below.
function Inverse function
----------- ------------------------
h h⁻¹
g g⁻¹
f f⁻¹
i i⁻¹
Answer:
The given functions and their corresponding inverses are correct.
Step-by-step explanation:
When deciding where to put an ordered pair on a graph its important to understand how ordered pairs work.
An ordered pair is split up into to pieces
(x,y) or number example (3,5)
When graphing the x coordinate will fall on your horizontal line or the line that looks like the horizon.
When graphing the y coordinate it will fall on your vertical line or the line that goes right up into the sky like a rocket.
To graph (3,5)
Go to the right 3 and up 5
Sometimes helps to use both fingers to keep your spot. Slide both fingers until they collide and that's where you would plot your point!
Hope this helps if you have an questions just comment and ill try to explain further.
Answer:
The speed of the wind is 40mph, the speed of the plane in still air is 360mph
Step-by-step explanation:
distance = speed * time
Both legs of the trip are 800 miles, let 'x' represent the speed of the plane in still air and 'w' represent the speed of the wind, then 'x+w' represents the speed with the wind and 'x-w' represents the speed into the wind
800 = (x-w)2.5
800 = (x+w)2
Rewrite equations:
800=−2.5w+2.5x;800=2w+2x
Steps: Solve 800=−2.5w+2.5x for w:
800=−2.5w+2.5x
800+2.5w=−2.5w+2.5x+2.5w(Add 2.5w to both sides)
2.5w+800=2.5x
2.5w+800+−800=2.5x+−800(Add -800 to both sides)
2.5w=2.5x−800
2.5w/2.5 = 2.5x - 800 / 2.5 (Divide both sides by 2.5)
w=x−320
Step: Substitute x−320 for w in 800=2w+2x:
800=2w+2x
800=2(x−320)+2x
800=4x−640(Simplify both sides of the equation)
800+−4x=4x−640+−4x(Add -4x to both sides)
−4x+800=−640
−4x+800+−800=−640+−800(Add -800 to both sides)
−4x=−1440
-4x/-4 = -1440/-4 (Divide both sides by -4)
x=360
Step: Substitute 360 for x in w=x−320:
w=x−320
w=360−320
w=40(Simplify both sides of the equation)
solving this system we have:
w=40
x=360
Therefore, the speed of the wind is 40mph, the speed of the plain in still air is 360mph
