What is the inverse of the function?
f(x) = 3^x + 1

f^-1(x)= log3 (x) +1
f^-1(x)= log3(x)-1

f^-1(x)=log3(x+1)

f^-1(x)=log3(x-1)

Answers

Answer 1

Answer:

f^-1(x)=logs3(x+1)

Step-by-step explanation:

Answer 2

Let y=f(x)

[tex]\\ \rm\Rrightarrow y=3^x+1[/tex]

Interchange

[tex]\\ \rm\Rrightarrow x=3^y+1[/tex]

[tex]\\ \rm\Rrightarrow lnx=ln(3^y+1)[/tex]

[tex]\\ \rm\Rrightarrow x=\dfrac{ln(y-1)}{ln3}[/tex]

Again interchange

[tex]\\ \rm\Rrightarrow f^{-1}(x)=\dfrac{ln(x-1)}{ln3}[/tex]


Related Questions

A Matrix of 1xM is called as ______.

Answers

Answer:

row matrix

Step-by-step explanation:

A matrix with only 1xmis called a ______ matrix

Darren’s taxable income is $27,481. He is filing as head of household, and he has already paid $3847 in federal taxes.

What will he receive or pay after he figures his taxes for the year?

Tax table of wages

He will receive a refund of $161.

He will receive a refund of $346.

He will pay $161.

He will pay $346.

Answers

Answer:

If Darren's taxable income is $27,481 and he is the head of household, he will be exempted from tax deductions. If he has already paid $3,847 in federal taxes, he will receive an equivalent amount in return if his tax deduction exceeds his collectible tax. Therefore, his money at the end of the year will total to $31,328.  

Step-by-step explanation:

Answer:

Step-by-step explanation:

he will receive a refund of 346 dollars

i just took the test

Part A and Part C the same? Why or why not?

Answers

Answer:

is part 1 and part 3 the same, no

Step-by-step explanation:

Answer:yes

Step-by-step explanation:

I'll give Brainliest, I need this now. :D​

Answers

Answer:

I think it's 6:3=18:9=54:27

Step-by-step explanation:

I hope this helps!

The model below represents an equation. IN Which represent like terms in the model of the equation? and and T Save and Exit Next Mark this and return Ei O Type here to search NEWD HELP ASAP PLSSS ​

Answers

Answer:

x x x and 1 1 1

Step-by-step explanation:

3rd option is the correct answer.

A department store sells shoes with an 70% markdown. If one pair of shoes is originally $148, then with the markdown, what is the new selling price for those shoes?

Answers

Answer:

$44.40

Step-by-step explanation:

100%-70%=30%

30/100x148=44.40 (discounted price)

Appreciate to be marked brainliest. Hope this helps!

2x=14−2
Find the value of x
Don't give wrong answer​

Answers

Answer:

[tex]\sf\longmapsto \: x = 6[/tex]

Step-by-step explanation:

[tex]\sf\longmapsto \: 2x = 14 - 2[/tex]

[tex]\sf\longmapsto \: 2x = 12[/tex]

[tex]\sf\longmapsto \: x = \frac{12}{2} [/tex]

[tex]\sf\longmapsto \: x = 6[/tex]

Answer:

x = 6

Step-by-step explanation:

Hey there,

[tex]2x =14-2\\2x=12\\\frac{2x}{2}=\frac{12}{2} \\x = 6[/tex]

Hope this helps you.

Let me know if you have any other questions :-)

Can you please Help me?

Answers

Answer:

D. 5i

Step-by-step explanation:

edge 2021

Solve the equation if 0°≤x≤360°*tan x =√3

Answers

Answer: This is a trig relationship from one of our special triangles, the 30-60-90 triangle.

Tan x = the opposite side of angle x divided by the adjacent side of angle x

The tangent is √3 when x = 60° or π/3

However, in this problem the value of the tangent is negative. In which of the four quadrants is the tangent function negative?

This function is negative in the second and fourth quadrants or when x = 120 and 300 degrees (or 2pi/3 and 5pi/3)

***I am assuming that the negative sign should be outside of the square root sign***

solve the following system of equations for all three variables.
-9x-y+2z= -4
-6x+y+5z= 2
-4x+y+5z= 6

Answers

Answer:

x=2, z=4, y=-6

Step-by-step explanation:

Add

-9x-y+2z= -4

-6x+y+5z= 2

-9x-6x is -15x

-y+y is 0

2z+5z is 7z

-4+2 is -2

So the equation now looks like this: -15x+7z=-2

Subtract

-6x+y+5z= 2

-4x+y+5z= 6

So the equation will look like this:

-6x+y+5z= 2

-(-4x+y+5z= 6)

-6x+4x is -2x

y-y is 0

5z-5z is 0

2-6 is -4

So the equation now looks like this: -2x=-4

You can find x by dividing -2 on both sides:

x=2

So 2 is x

Now you can substitute x into 2

-15(2)+7z=-2

-30+7z=-2

7z=28

Divide 7 on both sides:

z=4

So now you can substitute z into 4 (For any of the three equation)

-4(2)+y+5(4)=6

-8+y+20=6

20 minus 8 is 12

y+12=6

Subtract 12 on both sides:

y=-6

So the answers are

x=2, z=4, y=-6

Hope this helps!

Last year Kaitlin opened an investment account with $7600. At the end of the year, the amount in the account had increased by 6.5%. How much is this increase in dollars? How much money was in her account at the end of the year

Answers

The increase was: 494

Help me or I will steal your caprisun.

Answers

Answer:

C and D

Step-by-step explanation:

A. Incorrect as the directions are not opposite.B. Incorrect as - 40 - 10 = -50 m ≠ 0.C. Correct as the same amount is added and subtracted, resulting in zero.D. Correct as protons and electrons have opposite charges, their sum is neutral.

I when I'm 10, my brother is half of my age. How old is my brother if I am 44 now

Answers

Answer:

Step-by-step explanation:

A-B = 4–2 = 2 (age difference between A and B). IF A = 44,. B = A - 2 = 44 - 2 = 42 years old.

Answer:

39 years old

It could be;

10 ÷ 1/2 = 5

Age difference= 10 - 5= 5 years

So, 44 - 5 = 39 years old

Help very urgent, . . .

Answers

Answer: 3.1

Step-by-step explanation:


The answer is 3.1 hope this helps

How do I find the standard deviation?

Answers

Answer:

Step-by-step explanation:

Work out the Mean,

Then for every number, subtract the Mean and square the result.

Then work out the mean of those squared differences

and then take the square root of that.

What is formed when the number of electrons is changed?

Question 2 options:

isotope


radioisotope


a new element


ion

Answers

Answer:

A New Element

An ion is formed. Change of electrons = ionizing the element!

please help me with this sum​

Answers

Answer:

1. 384

2. 180

3. 324

4. 648

5. 476

6. 528

7. 294

8. 384

9. 414

10. 80

11. 72

12. 301

13. 222

14. 146

15. 156

16. 270

17. 283

18. 300

19. 292

20. 58

21. 64

22. 138

23. 296

24. 170

Hope it helps you

Gus wrote the following riddle: I am a number between 30 and 60. My ones digit is three less than my tens digit. I am a prime number.

What number does Gus’ riddle describe?

Answers

Answer: 41

Step-by-step explanation:

what is the expanded form of 203,574

Answers

Expanded Notation Form:

 203,574 =

 200,000  

+ 0  

+ 3,000  

+ 500  

+ 70  

+ 4  

Expanded Factors Form:

   203,574 =

 2 × 100,000  

+ 0 × 10,000  

+ 3 × 1,000  

+ 5 × 100  

+ 7 × 10  

+ 4 × 1  

Expanded Exponential Form:

 203,574 =

2 × 105

+ 0 × 104

+ 3 × 103

+ 5 × 102

+ 7 × 101

+ 4 × 100

200000+0+3000+500+70+4

can someone plz help me with this!!!

Answers

2 is the correct answer of this question

ANSWER QUICKLY!!!!!


Given the polynomial function


f(x)=x3−4x2+x+6


1) Name all of the possible rational roots for the function using the Rational Root Theorem.


2) Prove 2 is one of the zeroes of this function (show or describe your process).


3) Name all of the actual roots of this function and describe how you found them.


4) Write the original polynomial function f(x)=x3−4x2+x+6 in factored form.

Answers

Answer:

1. The possible roots are ±1, ±2, ±3, ±6. These are the factors of the trailing constant (6) divided by the factors of the leading coefficient (1). When the leading coefficient is 1, the possible roots are the factors of the constant

2. The polynomial is easier to evaluate when it is written in Horner form:

 f(x) = ((x -4)x +1)x +6

To show that 2 is a zero, we want to find f(2):

 f(2) = ((2 -4)2 +1)2 +6 = (-4 +1)2 +6 = -6 +6 = 0

 f(2) = 0, so 2 is one of the zeros of this function

3.  Using synthetic division (attached) or polynomial long division, we can divide the given polynomial by (x-2) to find the remaining factors. This division gives (x^2 -2x -3), which can be factored as (x -3)(x +1), so the three actual roots are ...

 x = 2 (from above), x = 3, x = -1 (from our factorization)

4. In factored form, the polynomial can be written ...

 f(x) = (x +1)(x -2)(x -3)

The first factor was found from the fact that 2 was given as a zero of the function. For any zero "a", a factor of the polynomial is (x-a).

The remaining factors were found by factoring the quadratic trinomial that resulted from the division of f(x) by x-2. That trinomial is x^2 -2x -3.

There are a number of methods that can be used to factor x^2 -2x -3. Again, the rational root theorem can help. It suggests that ±1 and ±3 are possible roots.

Find the mass of 250 ml of water. The density of water is 1 g/ml.
D= Density
M=
Volume - 10ml
What is the Mass?
V=
Mass - 70
Density
Alaalam

Answers

Answer:

250g

Step-by-step explanation :

250ml x 250g/ml = 250 g

To get the mass (in grams), you need to divide the ml's off and get the g alone.

If y varies directly with x which equation describes x = 72 and y = 36?

Answers

Answer:

k = 1/2

Step-by-step explanation:

direct variation equation is y = kx where 'k' is the constant of variation

substitute 36 for 'y' and 72 for 'x' to get:

36 = 72k

solve for 'k' to get:

k = 36/72 or k = 1/2

Use your expression from #2 to answer the following question. If there are 6 $5 bills and 4 $10 bills, how much money is in the box

Answers

There is 70$ in the box.

Answer:

70 dollars

Step-by-step explanation:

6 x 5 = 30, 4 x 10 = 40. Add them up, that's what you get.

solve pls brainliest

Answers

Answer:

53cm

Step-by-step explanation:

11+8+8+11+15=53cm

The answer above is correct

Plot the following and their opposites on the number line.

Answers

Step-by-step explanation:

Is there a image or any numbers because I can't see any

Answer:

If you are doing it thru edmentum the answer would be -2, 7, 1, 0, -5, 4, -3

Step-by-step explanation:

Hope this helps!!

A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is 100 m long and 60 m wide.
Find the area of the training field. Use the value 3.14 for , and do not round your answer. Be sure to include the correct unit in your answer.

Answers

Step-by-step explanation:

given,

length = 100 m

breadth = 60 m

we know,

area = l × b

now,

100 × 60 = 6000 m

therefore, area of rectangular field is 6,000 m.

and for both the semicircle if we add both the semicircle we will get a complete circle.

as the width of the rectangle is the diameter of circle so the radius of the circle is 60/2 = 30m

we know,

Area = πr²

now,

3.14 × 30²

3.14 × 900

2826 m

so,

area of rectangle + area of circle = area of the training field.

6000 + 2826 = 8826.

therefore, area of training field is 8,826 m.

hope this answer helps you dear...take care and may u have a great day ahead!

Answer:

8826 m²

Step-by-step explanation:

The field is composed of a rectangle and a circle .( the 2 semicircles form a complete circle when placed together )

area = area of rectangle + area of circle

        = lb + πr² ( r = 60 ÷ 2 = 30 )

        = (100 × 60) + (3.14 × 30²)

        = 6000 + (3.14 × 900)

        = 6000 + 2826

        = 8826 m²

You have a square table and want to create a
tablecloth for it using a piece of fabric.
The side length of the table is 72 inches. How
much fabric do you need?

Answers

Based on the information given, the length of fabric that's needed will be 288 inches.

From the information given in the question, we are informed that the side length of the table is 72 inches. Therefore, in order to calculate the fabric needed, we have to find the perimeter and this goes thus:

= 72 inches × 4

= 288 inches.

Therefore, the length of fabric that's needed will be 288 inches.

Read related link on:

https://brainly.com/question/24429956

What is the volume of the basement?

Answers

Volume = Length × Breadth × Height

So you are absolutely right, it is 252 yards squared

Hurry please What is the equation of this line
A. Y=1/4x-6
B. Y=6x-4
C. Y=6x-1/4
D. Y=4x-6

Answers

Sorry but it’s too confusing
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