All categories

2 years ago

Are f and g inverses of each other?

Mathematics

1 answer:

d1i1m1o1n [39]2 years ago

8 0

Answer:

The answer is: g ( x) and f ( x) are not inverses of each other.

Step-by-step explanation:

This is why you need to check both ways: sometimes there are fussy technical considerations, usually involving square roots, that force the composition not to work, because the domains and ranges of the two functions aren't compatible.

Hope this helps : )

You might be interested in

A cable car starts off with n riders. The times between successive stops of the car are independent exponential random variables

nikitadnepr [17]

Answer:

The distribution is $\frac{\lambda^{n}e^{- \lambda t}t^{n - 1}}{(n - 1)!}$

Solution:

As per the question:

Total no. of riders = n

Now, suppose the $T_{i}$ is the time between the departure of the rider i - 1 and i from the cable car.

where

$T_{i}$ = independent exponential random variable whose rate is $\lambda$

The general form is given by:

$T_{i} = \lambda e^{- lambda}$

(a) Now, the time distribution of the last rider is given as the sum total of the time of each rider:

$S_{n} = T_{1} + T_{2} + ........ + T_{n}$

$S_{n} = \sum_{i}^{n} T_{n}$

Now, the sum of the exponential random variable with $\lambda$ with rate $\lambda$ is given by:

$S_{n} = f(t:n, \lamda) = \frac{\lambda^{n}e^{- \lambda t}t^{n - 1}}{(n - 1)!}$

5 0

2 years ago

Flying against the wind, a jet travels 2160 miles in 3 hours. Flying with the wind, same jet travels 6000 miles in 6 hours. What

marissa [1.9K]

Answer:

The velocity of jet in still air is $860miles/hour$ and velocity of wind is $140miles/hour$ .

Step-by-step explanation:

Let x be the rate of the jet in still air and y be the rate of the wind.

Given:

Velocity against wind, a jet travels 2160 miles in 3 hours.

Velocity against wind $=\frac{2160}{3} = 720 miles/hour$

Flying with the wind, same jet travels 6000 miles in 6 hours.

Flying with the wind $=\frac{6000}{6} = 1000 miles/hour$

As such its velocity against wind is $x-y$

and with wind is $x+y$ therefore

$x-y=720$ ------------(1)

$x+y=1000$ ---------------(2)

Adding equation 1 and 2.

$2x=1720$

$x=\frac{1720}{2}$

$x=860$

Put x value in equation 2

$860+y=1000$

$y=1000-860$

$y=140$

Hence velocity of jet in still air is $860miles/hour$ and velocity of wind is $140miles/hour$ .

8 0

3 years ago

In the figure,BC andAD are line segments. What is the sum of x and y?

Alika [10]

Can you please post the image.

7 0

3 years ago

Your electric bill has been as follows for the past six months:

kakasveta [241]

You want to find the monthly average over the past 6 months.

July: $78.56

August: $30.21

September: $81.20

October: $79.08

November: $66.18

December: $100.75

Add all of these up

(July) $78.56

(August) $30.21

(September) $81.20

(October) $79.08

(November) $66.18

(December) + $100.75

----------------------------------------------

(Total cost) $435.88

There are 6 months you are calculating for, therefore divide the total (combined) cost of 6 months with the total number of months (in this case, 6)

$435.88 (total cost of 6 months) ÷ 6 (months)

The average cost per month of over the past 6 months is $72.66.

4 0

3 years ago

Read 2 more answers

The volume of the right triangular prism is 91.8ft. The height of the prism is 10.8ft. What is the area of each base? Show your

kaheart [24]

Answer:

8.5 ft.

Step-by-step explanation:

We'll use this right triangular prism volume formula: base area x height = volume

base area = ?

length = 10.8

volume = 91.8

base area x 10.8 = 91.8

Divide both sides by 10.8

base area x 10.8/10.8 = 91.8/10.8

base area = 8.5

4 0

2 years ago