What is the volume, in cubic feet, of this composite figure? (Do not write

Determine the domain of the function (fog)(x) where f(x)=3x-1/x-4 and g(x)=x+1/x

Katarina [22]

Answer: (-∞,-1) ∪ (0,+∞)

Step-by-step explanation: The representation fog(x) is a representation of composite function, meaning one depends on the other.

In this case, fog(x) means:

fog(x) = f(g(x))

fog(x) = $3(x+\frac{1}{x} )-\frac{1}{x+\frac{1}{x} } -4$

$fog(x)=3x+\frac{3}{x} -\frac{1}{\frac{x^{2}+x}{x} } -4$

$fog(x)=3x+\frac{3}{x} -\frac{x}{x^{2}+x} -4$

$fog(x)=\frac{3x^{2}(x^{2}+x)+3(x^{2}+x)-x-4x(x^{2}+x)}{x(x^{2}+x)}$

$fog(x)=\frac{3x^{4}+3x^{3}+3x^{2}+3x-x-4x^{3}+4x^{2}}{x(x^{2}+x)}$

$fog(x)=\frac{3x^{4}-x^{3}-x^{2}+2x}{x(x^{2}+x)}$

This is the function fog(x).

The domain of a function is all the values the independent variable can assume.

For fog(x), denominator can be zero, so:

$x(x^{2}+x) \neq 0$

If x = 0, the function doesn't exist.

$x^{2}+x \neq0$

$x(x+1) \neq0$

$x+1\neq0$

$x\neq-1$

<u>Therefore, the domain of this function is: </u><u>-∞ < -1 or x > 0</u>

5 0

3 years ago

Triangle ABC is shown below. Using a compass and straightedge, construct the dilation of ABC centered at B with a scale factor o

qaws [65]

Triangle ABC would remain the same because a dilation generally preserves the measure of an angle.

<h3>What is scale factor?</h3>

A scale factor simply refers to a ratio of two (2) corresponding side lengths or diameter in two (2) similar geometric figures such as triangles.

In this exercise, you're required to construct a dilation of triangle ABC that is centered at B with a scale factor of 2 by using a compass and straightedge.

In conclusion, triangle ABC would remain the same because a dilation generally preserves the measure of an angle.

Read more on scale factor here: brainly.com/question/2826496

#SPJ1

4 0

2 years ago

Jade buys a blouse and a skirt for 3/6 of their original price. Jade pays a total of $31 for the two items. If the original pric

Damm [24]

Answer:

3/4 times 18= 13.5

31.5-13.5=18

It cost 18 dollars for the skirt with a discount.

It cost 13.5 for the blouse as opposed to the original price of 18 dollars.

18(skirt)+13.5(blouse)=31.5

If you set up a proportion to find the original price of the skirt you will get the answer.

18/x=75/100

75x=18 times 100

75x=1800

75x/75=1800/75

x=24

The original price of the skirt is 24 dollars.

Step-by-step explanation:

4 0

3 years ago

F(x)= \frac{ \sqrt{x-6} }{ \sqrt{x-4}

Bingel [31]

Answer:

Hi!

Step-by-step explanation:

i would love to help you, but i don't quite understand the question.

Could you please tell me so i can better help you?

8 0

3 years ago

Read 2 more answers

. What is the minimum number of rows of bricks

vova2212 [387]

Answer: 22 rows

Step-by-step explanation: Divide 48 by 2.25 and round up.

Hope this helps, have a good day

3 0

3 years ago