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3 years ago

BRAINIEST ANSWER QUICKKKK!!!!! Which of these pairs of functions are inverse functions use: a b c or d

Mathematics

1 answer:

sveticcg [70]3 years ago

4 0

We'll call the result of the original function f and the argument g for sanity.

f = 2^{g-1} + 1

f-1 = 2^{g-1}

log2 (f-1) = g-1

g = 1 + log2 (f-1)

Not a, wrong sign on the -1 at the end.

f = 1/2 (ln(g/2) -1 )

2f = ln(g/2) -1

2f + 1 = ln(g/2)

g/2 = e^{2f + 1}

g = 2 e^{2f + 1}

b is a good pair of inverses, at least over the domain of the logarithm.

f = 4 ln(g^2)/e^2

fe^2 = 4 ln(g^2)

fe^2/4 = ln g^2

g^2 = e^{(fe^2)/4}

Now we take the square root so

$g = \pm \sqrt{ e^{(fe^2)/4} }
$

The $\pm$ is telling us f is not one-to-one on its domain so doesn't have a true inverse.

f = 10^{g-10} - 10

f + 10 = 10^{g-10}

log(f+10) = g-10

g = 10 + log(f+10)

wrong sign again.

I'll go with choice B.

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Question 1: Explain how the letter x (or any letter) is used when writing expressions, and give an example. How are expressions

BaLLatris [955]

Answer:

Question 1:

The letter x or any letter used when writing an expression is representative of unit of an idea, quantity or measure, such that it can be translated in the expression to provide information about a related idea

Question 2:

The expression can be translated as two times the expression three (variable) x minus two (variable) y plus the constant 7

Question 3:

In the first expression, the like terms are;

10y and (-2y),

3x and x

In the second expression, the like terms are;

-y and -2y

3x and 4x

The first expression simplifies to 8y + 4x + 10

The second expression simplifies to 7x - 3y + 6

Question 4:

The expression is evaluated as 122

Question 5:

The equivalent expression of the expression 3(4x + 2y) + 5x, is 17x + 6y

To prove when x = 1 and y = 2 we have;

3(4×1 + 2×2) + 5×1 is 29

17×1 + 6×2 is 29 which are equivalent in value

Step-by-step explanation:

Question 1:

Example;

If x is the symbol representing the average number of oranges sold in 1 hour, then the expression for the number of oranges sold per day of 24 hours = 24·x

An expression is a written mathematical symbolic statement that shows the the finite merging together of representative symbols by the mathematical operations that govern the present constraints

An equation is a statement that two expressions are equal

Question 2:

The given expression is 2(3x - 2y) + 7

The parts are;

The coefficient of (3x - 2y) = 2

The constant term = 7

The variables are x and y

Which gives

The coefficient of the variable x = 6

The coefficient of the variable y = -4

The expression can be translated as two times the expression three (variable) x minus two (variable) y plus the constant 7

The expression can be translated as two times the bracket open three times (variable) x minus two times (variable) y bracket close plus the constant 7

The expression can be expanded as 2(3x - 2y) + 7 → 6·x - 4·y + 7 which is expressed verbally as follows;

Six times (variable) x minus four times (variable) y plus the constant 7

Question 3:

The expressions are;

10y + 3x + 10 + x - 2y..........................(1)

3x - y + 4x + 6 - 2y,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,(2)

In the first expression, the like terms are;

10y and (-2y),

3x and x

In the second expression, the like terms are;

-y and -2y

3x and 4x

They are like terms because they can be simply added together to simplify the expressions as follows

10y + 3x + 10 + x - 2y gives 10y - 2y + 3x + x 10 to give 8y + 4x + 10

Also

3x - y + 4x + 6 - 2y gives 3x+ 4x - y - 2y + 6 to give 7x - 3y + 6

Question 4:

The expression 8x² + 25·y when x = 3 and y = 2 is evaluated by replacing (putting) the value x and y (into the expression)

The expression is then evaluated as 8×3² + 25×2 which is the same as 72 + 50 or 122

Question 5:

To write the equivalent expression of the expression 3(4x + 2y) + 5x, we expand the expression as follows;

3×4x + 3×2y + 4x which is 12x + 6y + 4x

We combine like terms;

12x + 5x + 6y which is 17x + 6y

To prove we can check by substituting a value for each of the variables x and y such as x = 1 and y = 2

3(4×1 + 2×2) + 5×1 is 29

17×1 + 6×2 is 29

5 0

4 years ago

A square has a perimeter of 18cm. How long is the side of the square? 15 POINTS**

emmainna [20.7K]

Answer:

Each side is 4.5 cm

Step-by-step explanation:

$18 \div 4 = 4.5$

To find the perimeter of a square you add all the sides.

But to find the side length you do the opposite. Which is the equation above.

Hope this helps : )

5 0

3 years ago

Please help very urgent

Alik [6]

Answer:

32, 16, 8, 4, 2, 1

Explanation:

The geometric mean can be represented by $\sqrt[n]{x_{1} • x_{2} • x_{3} • .. x_{n}}$ .

Which is the mean of the product of n numbers, used to find the average of a geometric progression.

Don't get confused by geometric mean, it is only asking you about the next numbers in the geometric sequence given the first and sixth term.

The explicit rule for a geometric sequence can be modeled by:

$a_{n} = a_{1} • r^{n-1}$

Where $a_{n}$ is the nth term, $a_{1}$ is the first term in the sequence, n is the term number, and r is the common ratio.

Since we already know the first term, $a_{1}$ will simply be 32.

Since we know it's geometric, there will be an exponential relationship, which means that we will use the geometric mean to find the common ratio.

There are 6 total terms, r is raised to the n – 1 so 6 – 1 = 5, and that will be the degree of this root.

$\sqrt[5]{\frac{a_{6}}{a_{1}}}$ =

$\sqrt[5]{\frac{1}{32}}$ =

$\frac{1}{2}$ .

Therefore: $r = \frac{1}{2}$ .

Using all the information we have, we can find the explicit rule:

$a_{n} = a_{1} • r^{n-1}$

$a_{1}$ = 32
$r = \frac{1}{2}$

$a_{n} = a_{1} • r^{n-1}$ →

$\boxed{a_{n} = 32 • (\frac{1}{2})^{n-1}}$

________________________________

We can test that this works by substituting the number location of the term you want to find.

For instance:

$a_{1} = 32 • (\frac{1}{2})^{1-1}$

$a_{1} = 32 • (\frac{1}{2})^{0}$

$a_{1} = 32 • 1$

$a_{1} = 32$

$a_{6} = 32 • (\frac{1}{2})^{6-1}$

$a_{6} = 32 • (\frac{1}{2})^{5}$

$a_{6} = 32 • \frac{1}{32}$

$a_{6} = 1$

3 0

3 years ago

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Evaluate 8j - k + 14 when j = 0.25 and k = 1.

pantera1 [17]

Steps to solve:

8j - k + 14; j = 0.25 and k = 1

~Substitute

8(0.25) - (1) + 14

~Simplify

2 - 1 + 14

~Subtract

1 + 14

~Add

Best of Luck!

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dezoksy [38]

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Step-by-step explanation:

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