How to explain your work in division

Given f(x)=x3 and g(x)= 1-5x2, fine (fog)(x) and it’s Domain

andre [41]

Answer:

Option B. $f(g(x)) = (1-5x ^ 2) ^ 3$ all real numbers

Step-by-step explanation:

We have

$f(x) = x ^ 3$ and $g(x) = 1-5x ^ 2$

They ask us to find

(fog)(x) and it's Domain

To solve this problem we must introduce the function g(x) within the function f(x)

That is, we must do f(g(x)).

So, we have:

$f(x) = x ^ 3$

$g(x) = 1-5x ^ 2$

Then:

$f(g(x)) = (1-5x ^ 2) ^ 3$

The domain of the function f(g(x)) is the range of the function $g(x) = 1-5x ^ 2$ .

Since the domain and range of g(x) are all real numbers then the domain of f(g(x)) are all real numbers

Therefore the correct answer is the option b: $f(g(x)) = (1-5x ^ 2) ^ 3$

And his domain is all real.

5 0

3 years ago

Read 2 more answers

Ann is 5 feet 3 inches tall. To find the height of a lamppost, she measured her shadow to be 8 feet 9 inches and the lamppost’s

Makovka662 [10]

Answer: The lamppost is 7 feet 2 inches

Step-by-step explanation: If Ann measured her own height and her shadow, then what she used is a ratio between both measurements. If she can measure the shadow of the lamppost, then she can use the same ratio of her height and it’s shadow to derive the correct measurement of the lamppost.

If Ann’s height was measured as 5 feet 3 inches, and her shadow was 8 feet 9 inches, the ratio between them can be expressed as 3:5.

Reduce both dimensions to the same unit, that is, inches. (Remember 12 inches = 1 foot)

Ratio = 63/105

Reduce to the least fraction

Ratio = 3/5

If the height of the lamppost is H, then

H/144 = 3/5

H = (144 x3)/5

H = 86.4

Therefore the lamppost is approximately 86 inches, that is 7 feet and 2 inches tall.

5 0

3 years ago

Working his way through school, Joe works two part-time jobs for a total of 18 hours a week. Job A pays $5.70 per hour, and Job

ad-work [718]

Answer:

A = 14.2/1.1 hours

B = 5.091 hours

Step-by-step explanation:

Formulate 2 simultaneous equations

5.7A + 6.8B = 111.40..........(1)

A +B =18...............................(2)

Multiply each item in (2) by 5.7 to get

5.7A + 5.7B = 97.2............(3)

subtract (1) - (3) on each side

5.7A -5.7A + 6.8B - 5.7B = 111.40 -97.2

1.1B = 14.2

B = 14.2 /1.1

to get A use equation (2)

A = 18 - B

A = 18 - 14.2/1.1 = 5.091

4 0

3 years ago

Read 2 more answers

How do you find x? and how do you round to the nearest tenth?

expeople1 [14]

Hey there!

In order to solve this problem, we can use the Pythagorean Theorem, which is $c^2 = a^2 + b^2$ . Since the Pythagorean Theorem would find only half of the length of x, we'll need to double it in the end.

First, let's plug in what we know to the Pythagorean Theorem: $2.1^2 = 1.4^2 + b^2$

Next, we'll simplify to that $b^2$ is by itself:

$b^2 = 2.45$

Then, we'll find the square root of 2.45, multiply that by 2 and round to the nearest tenth:

$2(\sqrt{2.45} ) = 3.1$

Therefore, x = 3.1 ft.

How to round to the nearest tenth:

In a decimal, the tenth is the first number after the decimal point. To round to the tenth, if the number in the hundredth place is less than 5, you keep the number as it is, but if the number in the hundredth place is more than 5, you increase the number in the tenth place by 1.

Hope this helps!! :)

6 0

3 years ago

At the movie theatre, child admission is $5.20 and adult admission is $8.60. On Sunday, 132 tickets were sold for a total sales

xxMikexx [17]

Answer:

60 tickets for children were sold

Step-by-step explanation:

Let x be the number of sold children's tickets and let y be the number of adult tickets sold, then we can pose the following equations.

$x + y = 132$ (i) Because 132 tickets were sold in total