4x+5=6x-7
How do I solve this?

The inverse function of the given function is

              f ⁻¹(x)  = x³ + 15x² + 75x + 123

What are inverse functions?

A function that can reverse into another function is known as an inverse function or anti-function. In other words, the inverse of a function f will take y to x if any function f takes x to y. When a function is written as f or F, its inverse is written as f⁻¹ or F⁻¹.

The given function is ∛(x+2) - 5

One of the properties of the inverse function is

f( f ⁻¹ x) = x

We utilise this property to find f ⁻¹ x.

f(x) = ∛(x+2) - 5

f( f ⁻¹x) = ∛( f ⁻¹(x) + 2) - 5

Using the above property

x = ∛( f ⁻¹(x) + 2) - 5

x + 5 = ∛( f ⁻¹(x) + 2)

Cubing both sides,

(x+5)³ =  f ⁻¹(x) + 2

x³ + 15x² + 75x + 125 = f ⁻¹(x)  + 2

f ⁻¹(x)  = x³ + 15x² + 75x + 123

Therefore the inverse function of the given function is

              f ⁻¹(x)  = x³ + 15x² + 75x + 123

To learn more about inverse functions, follow the link.

https://brainly.com/question/3831584

#SPJ1

To prove that T is a linear transformation, we need to show that T(c~u + ~v) = cT(~u) + T(~v) for any scalar c and any vectors ~u and ~v in R2.

Let ~u = (u1, u2) and ~v = (v1, v2) be two vectors in R2 and let c be any scalar. Then,

T(c~u + ~v) = T(cu1 + v1, cu2 + v2) = (3(cu1 + v1) - 2(cu2 + v2), 2(cu2 + v2))

= (3cu1 + 3v1 - 2cu2 - 2v2, 2cu2 + 2v2)

= (3cu1 - 2cu2, 2cu2) + (3v1 - 2v2, 2v2)

= c(3u1 - 2u2, 2u2) + (3v1 - 2v2, 2v2)

= cT(~u) + T(~v)

Therefore, T is a linear transformation.

To find the standard matrix A of T, we can use the fact that T(~e1) and T(~e2) are the first and second columns of A, respectively, where ~e1 = (1, 0) and ~e2 = (0, 1) are the standard basis vectors of R2.

T(~e1) = T(1, 0) = (3(1) - 2(0), 2(0)) = (3, 0)

T(~e2) = T(0, 1) = (3(0) - 2(1), 2(1)) = (-2, 2)

Therefore, the standard matrix A of T is:

A = [ 3  -2 ]
     [ 0   2 ]

To determine if T is one-to-one, we can use the fact that a linear transformation is one-to-one if and only if its standard matrix A has linearly independent columns. In this case, the columns of A are linearly independent because they are not scalar multiples of each other. Therefore, T is one-to-one. Alternatively, we can use the fact that a linear transformation is one-to-one if and only if its standard matrix A has a nonzero determinant. In this case, the determinant of A is (3)(2) - (0)(-2) = 6, which is nonzero. Therefore, T is one-to-one.

Know more about linear transformation here:

https://brainly.com/question/30585642

#SPJ11

Answer:

Store 1

Step-by-step explanation:

store 2. tv is 250

250+25%

250+62.50=312.50

The correct option is False. Sampling only seniors at Dr. Khan's college may not provide a representative sample of how all college students in her state will vote during the next election.

The sample may not capture the diversity and demographics of college students in the entire state. To obtain a more representative sample.

It would be necessary to consider a broader range of colleges and universities and potentially include students from various backgrounds and institutions within the state.

To know more about diversity visit-

brainly.com/question/4066057

#SPJ11

Answer:

9x-10

Step-by-step explanation:

(4x+10) - (-5x+20)

Open the brackets

4x+10+5x-20

Collect like terms

4x+5x+10-20

9x-10

Answer: 31.5

Step-by-step explanation:  
6*4=24 (Shaded Rectangle)

3*5=15  15/2=7.5 (Shaded Triangle)
7.5 + 24 = 31.5

Answer:

x < \(\frac{6}{7}\)

Step-by-step explanation:

2(1 - 3x) - (x - 5) > 1 ← distribute parenthesis and simplify left side

2 - 6x - x + 5 > 1

- 7x + 7 > 1 ( subtract 7 from both sides )

- 7x > - 6

divide both sides by - 7, reversing the symbol as a result of dividing by a negative quantity.

x < \(\frac{6}{7}\)

Answer:

x < (6/7)

Step-by-step explanation:

2(1-3x)-(x-5)>1

2 - 6x -x + 5 > 1

-7x + 7 > 1

-7x > -6

x < (6/7)     [The inequality is reversed when dividing or multiplying with a negative value]

The answer of the given question based on models are , Model 1 = e⁽⁽ˣ⁻³⁾/²⁾ , Model 2 = (x/3)³ - 4 , Model 3 =  (15x-y)/(y-5) .

An inverse function is a function that undoes the effect of another function. Specifically, if a function f maps an input value x to an output value y, then the inverse function f⁻¹ maps the output value y back to the original input value x. In other words, the inverse function "reverses" the mapping of the original function.

In each of these models, the inverse function f⁻¹(x) represents the input value (x) that would yield a particular output value (y) of the original function f(x).

In Model 1, the inverse function f⁻¹(x) is  e⁽⁽ˣ⁻³⁾/²⁾, which represents the number of hours required to produce a certain amount of fresh water. The inverse function allows us to determine how long it would take to produce a specific amount of fresh water, given the rate of production provided by the original function.

In Model 2, the inverse function f⁻¹(x) is (x/3)³ - 4, which represents the number of units of product A needed to generate a certain amount of profit. The cube root function is used to represent the relationship between the profit and the number of units sold. The inverse function allows us to determine how many units need to be sold to achieve a specific level of profit.

In Model 3, the inverse function f⁻¹(x) is (15x-y)/(y-5), where y represents the number of penguins. This function represents the number of years that have passed since 2012 to achieve a certain population of penguins. The rational function is used to represent the relationship between the population of penguins and the number of years that have passed. The inverse function allows us to determine how many years have passed to achieve a specific population of penguins.

Overall, the inverse function provides a way to determine the input value that corresponds to a particular output value of the original function. This information can be useful in understanding the behavior and relationships between variables in each of these models.

To know more about Function visit:

https://brainly.com/question/10500042

#SPJ1

Answer: Answer and explanation in picture

Step-by-step explanation:

Answer: $13.5

Step-by-step explanation:

1. 15 x 10 =150

2. 150/100=1.5

3. 15.00 - 1.50= 13.5

Complexes with a coordination number 4 mostly adopt tetrahedral and squar planar geometries.

Complexes with a coordination number 4 mostly adopt tetrahedral and squar planar geometries.

To learn more about geometries, refer to:

https://brainly.com/question/19241268

#SPJ4

Answer:

2,733.25 pizzas (or 2,734 if whole number is needed)

Step-by-step explanation:

13 377

94.25 x

13x = 35532.25

x = 2733.25

Answer:

40 tickets

Step-by-step explanation:

2800 = 70x

x is the number of tickets. You have to solve for x

Divide each side by 70

2800/70 = 70x/70

40 = x

Answer:

Step-by-step explanation:

To solve the system of equations by combining the equations, we can use the method of elimination:

x + 2y = -14 (equation 1)

-4x - y = 28 (equation 2)

We can eliminate y by multiplying equation 1 by 4 and adding it to equation 2:

4x + 8y = -56 (4 * equation 1)

-4x - y = 28 (equation 2)

7y = -28

Solving for y, we get:

y = -4

Substituting this value into equation 1, we get:

x + 2(-4) = -14

Solving for x, we get:

x - 8 = -14

x = -6

Therefore, the solution to the system of equations is x = -6 and y = -4.

Step-by-step explanation:

Absolute value function:

Swim 3 feet under water => |-3|

Stand 20 feet above => |20|

Using the absolute value function,

we have |-3| = 3 and |20| = 20.

Since 3 is less than 20, |-3| < |20|. (C)

Answer:

63.4°

Step-by-step explanation:

y = 2x - 1

dy/dx = 2

∴ The angle is arc tan(2) = tan^-1(2) = 63.4°

Answer: Length=6

Step-by-step explanation:

The simplified expression for (f ∘ g)(x) is 2 + x (option d).

To find and simplify (f ∘ g)(x), we need to substitute the expression for g(x) into f(x) and simplify.

Given:

f(x) = log₃(9x)

g(x) = \(3^x\)

Substituting g(x) into f(x):

(f ∘ g)(x) = f(g(x)) = log₃\((9 * 3^x)\)

Now, we simplify the expression:

log₃\((9 * 3^x)\) = log₃(9) + log₃\((3^x)\)

Since logₓ(a * b) = logₓ(a) + logₓ(b), we have:

log₃(9) + log₃\((3^x)\) = log₃\((3^2)\) + x

Using the property logₓ\((x^a)\) = a * logₓ(x), we get:

log₃\((3^2)\) + x = 2 * log₃(3) + x

Since logₓ\((x^a)\) = a, where x is the base, we have:

2 * log₃(3) + x = 2 + x

Therefore, (f ∘ g)(x) simplifies to:

(f ∘ g)(x) = 2 + x

So, the correct answer is (d) 2 + x.

To know more about expression, refer here:

https://brainly.com/question/31800038

#SPJ4

Complete Question:

Given f(x)=log₃(9x) and g(x)=\(3^x\). Find and simplify (f ∘ g)(x)

(a) 2x

(b) x

(c) \(27^x\)

(d) 2+x

(e) None of these.

If we repeated this procedure many times, the average number of points scored by our sample of 30 students will be between 344 and 406 points approximately 90% of the time.

This means that we are 90% confident that the true population mean of points scored by all students at the high school falls within this range based on the sample of 30 students who played the game for an hour.
A random sample of 30 students at a high school was allowed to play a popular cell phone game for an hour, yielding an average score of 375 with a standard deviation of 100. The 90% confidence interval is 375 ± 31. The statement that best summarizes the meaning of this confidence interval is: If we repeated this procedure many times, the average number of points scored by our sample of 30 students will be between 344 and 406 points approximately 90% of the time.

Visit here to learn more about population:

brainly.com/question/27991860

#SPJ11

the length of the sections will be 24 and 18 respectively.

Parallel lines are lines in a plane that are always the same distance apart. Parallel lines never intersect. Perpendicular lines are lines that intersect at a right (90 degrees) angle.

Given, Some pair of lines in that three lines are parallel and two of them are intersecting them.

Since, these are the the section made by two parallel lines. Thus, these given section will be Proportional to each other.

Thus,

20/15 = ( 7x - 11)/(4x - 2)

4/3 = ( 7x - 11)/(4x - 2)

16x - 8 = 21x - 33

5x = 25

x = 5

therefore, the length of the sections will be 24 and 18 respectively.

Learn more about parallel lines here:

https://brainly.com/question/28969931

#SPJ1

Therefore, the value of n that makes the system of equations true is n = 10.

Given:

p = 2n

p - 5 = 1.5n

Substituting the value of p from the first equation into the second equation, we have:

2n - 5 = 1.5n

Next, we can solve for n by subtracting 1.5n from both sides of the equation:

2n - 1.5n - 5 = 0.5n - 5

Simplifying further:

0.5n - 5 = 0

Adding 5 to both sides of the equation:

0.5n = 5

Dividing both sides by 0.5:

n = 10

Therefore, the value of n that makes the system of equations true is n = 10.

Learn more about equations here

https://brainly.com/question/29657992

#SPJ11

T is the linear transformation described by T(w,z) in L(C2). This indicates that the linear transformation T changes two-dimensional vectors of the type (w,z) to (-z,w).

To get T's eigenvalues, solve the equation T(v) = v, where is the eigenvalue and v is the eigenvector. By solving this equation, we discover that T's eigenvalues are λ1 = -1 and λ2 = 1.

For each eigenvalue, the associated eigenspaces are the subspaces of C2 that are spanned by the eigenvectors of T. The eigenspace is the subspace covered by the eigenvector λ1= -1 is (1,0). The eigenspace is the subspace spanned by the eigenvector λ2= 1 is (0,1).

As a result, the subspaces covered by (1,0) and (1,1) are the generalized eigenspaces corresponding to the different eigenvalues of T. (0,1).

Learn more about eigenvalues here:

https://brainly.com/question/15423383

#SPJ4

The number of pounds that can be loaded on the elevator safely must be less than 600 pounds.

Inequality is simply a type of equation that does not have an equal sign in it. Inequality is defined as a statement about the relative size as well as is used to compare two statements.

The number of pounds that can be safely loaded onto an elevator, x, can be represented by the inequality 2x <1,200.

Then the value of the x will be

2x < 1200

 x < 600

Then the number of pounds that can be loaded on the elevator safely must be less than 600 pounds.

More about the inequality link is given below.

https://brainly.com/question/19491153

#SPJ2

Answer:

The one in yellow is the answer.

Step-by-step explanation:

Hope this helped!

Answer:

D.

Step-by-step explanation:

x + 6 ≤ 8

subtract 6 on both sides.

x ≤ 2

Option D is the correct answer.

Answer:

He will earn $140, my bad miss calculated...

Step-by-step explanation:

Its 140....

Answer: 3) cos 46 degrees

Step-by-step explanation:

Answer:

y = x - 3

Step-by-step explanation:

a linear equation has the form

y = ax + b

the only equation in this form is

y = x - 3

Answer:

what exactly are we classifying here, angle? Shape?

Answer:

-8

Step-by-step explanation:

Answer: The inequality or equality that describes the situation "Ginnie is over 60 years of age" is:

D. x ≥ 60

This means that Ginnie's age, represented by x, is greater than or equal to 60 years.

Step-by-step explanation: