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4 years ago

WILL GIVE BRAINLIEST!

Mathematics

1 answer:

Alchen [17]4 years ago

7 0

Answer:

A.The functions f(x) and g(x) are inverses of each other

B. x∈ (-∞ , 0) ∪ (0 , 2) ∪ (2, +∞)

Step-by-step explanation:

To prove the above, we use the following formula:

f⁻¹( f(x) ) = x

where f⁻¹(x) is inverse function and f(x) is original function

In this case we use f(x) as inverse function and g(x) as original function

Composition of functions is:

f(g(x)) = f((2x+1)/x) = 1/(((2x+1)/x) -2) = 1/((2x+1-2x)/x) = 1/(1/x) = x

We get x finally and prove that these functions are inverses to each other.

B. Composition of the functions are possible under following conditions:

x -2 ≠ 0 and x ≠ 0 namely x ≠ 2 and x ≠ 0

Domain is x∈ (-∞ , 0) ∪ (0 , 2) ∪ (2, +∞)

God with you!!!

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Mark is on the wrestling team. He weighs 125 pounds but wants to gain some weight. Each week

harkovskaia [24]

Answer:

Step-by-step explanation:

1) create equation

y = (4)2.5 + 125

2) simplify

y = 10 + 125

y = 135

3) find difference

x = 135-125/125

x = 0.08

x = 8%

4 0

2 years ago

a group of students attend a math club half the students are boys and 4/9 of the boys have brown eyes what fraction of the group

enyata [817]

From the whole group half the club are boys.
fraction of boys from the whole class = 1/2
from this fraction, 4/9th of the boys have brown eyes
therefore fraction of boys who have brown eyes
= 4/9 of 1/2
the 'of' function is used to multiply
$\frac{4}{9} * \frac{1}{2}$
when multiplying fractions numerators are multiplied by numerators and denominators multiplied by denominators
$\frac{4*1}{9*2} = \frac{4}{18}$
4/18 can be simplified by dividing the whole number by a common number
4/18 divided by 2 = 2/9
the answer is 2/9
2/9 of the club are boys with brown eyes

3 0

3 years ago

Read 2 more answers

Nguyen is decorating the room for her sister’s baby shower party. She is wrapping Vietnamese conical hats in baby prints tissue

kodGreya [7K]

Answer:

She needs 301.8 in² of tissue paper.

Step-by-step explanation:

In order to calculate the amount of tissue paper she needs to make 21 hats, we need to find the area of each hat and multiply it by the total number of hats she wants to make.

Since the Vietnamese conical hats are hollow and don't have a base, we need to find the area of the it's lateral walls, this is given by the following expression:

lateral area = pi*r*l

r = d/2 = 16/2 = 8 in

We were given the height, but we need the slant height, therefore:

l = sqrt(r² + h²) = sqrt(8² + 9²) = sqrt(64 + 81) = sqrt(145) = 12.041 in

Then the lateral area is:

lateral area = pi*8*12.0141 = 301.8 in²

She needs 301.8 in² of tissue paper.

4 0

3 years ago

46 2/3% of 28 please i need to know answer an work

Bogdan [553]

First, it would help to put 46 and 2/3 into an improper fraction: 140/3.

Then, since this is a percent, we put that improper fraction over 100: (140/3)/100 = 140/300.

Finally, we multiply this answer by 28 since "of" means multiply:

(140/300) * 28 = 196/15 = 13 1/15

8 0

3 years ago

Find f'(x) and state the domain of f': f(x) = In (2x^2+1)

-Dominant- [34]

Answer:

$f'(x) = \frac{4x}{2x^2+1}$

Domain: All Real Numbers

General Formulas and Concepts:

Algebra I

Domain is the set of x-values that can be inputted into function f(x)

Calculus

The derivative of a constant is equal to 0

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Chain Rule: $\frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Derivative: $\frac{d}{dx} [ln(u)] = \frac{u'}{u}$

Step-by-step explanation:

Step 1: Define

f(x) = ln(2x² + 1)

Step 2: Differentiate

Derivative ln(u) [Chain Rule/Basic Power]: $f'(x) = \frac{1}{2x^2+1} \cdot 2 \cdot 2x^{2-1}$
Simplify: $f'(x) = \frac{1}{2x^2+1} \cdot 4x$
Multiply: $f'(x) = \frac{4x}{2x^2+1}$

Step 3: Domain

We know that we would have issues in the denominator when we have a rational expression. However, we can see that the denominator would never equal 0.

Therefore, our domain would be all real numbers.

We can also graph the differential function to analyze the domain.

5 0

3 years ago