What are the domain and range of f (x) = log (x 6) minus 4?

Answers

Answer 1

Answer:

We will see that the domain of the function is:

D: {x | x ∈ R | x > -6}

How to find the domain of a function?

To find the domain of a function, we start by assuming that it is the set of all real numbers, and then we remove the problematic points.

In this case, we have a logarithm, and as you may remember, we can only evaluate the logarithm in positive values, so we need to remove all the values of x such that:

x + 6 ≤ 0

Solving for x, we get:

x ≤ -6

So the only values of x allowed are the ones that make the next inequality true:

x > -6.

Thus we can write the domain as:

D {x | x ∈ R | x > -6}

Where the second part, x ∈ R, is usually ignored, as we assume that x is a real number unless we specify that it is not, but just for completion, I wrote it.


Related Questions

30 POINTS !! HELP ME PLEASE! WILL GIVE BRAINLIEST TO BEST ANSWER
SHOW STEPS PLEASE! THANK YOU SOO MUCH!

Solve the system of equations

{3x−y=6
{6x+y=21

Answers

Answer:

The easiest way to solve this is by elimination.  

3x - y = 6  

6x + y = 21

Since you have a negative and positive y with the same coefficients (1), they cancel, and you add the other terms so it would look like:

9x = 27  

Then solving for x leaves you with x = 3  

Then you take the x value of three and plug it into to either of the equations, so  

3(3) - y = 6

9 - y = 6  

subtracting 9  

-y = -3  

then dividing by -1  

y = 3  

so the solution is x = 3 y = 3 or (3,3)  

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

Add 3x + 6x, and execute the y, then -6 from 21 and you got ur answer of 15!

The total of sixty three and a number *
1 point
63 + n
n63
63 - n
63/n

Answers

63+n

Have an amazing day!

Solve the system of linear equations by elimination. Write your answer in the form (x,y)
-7x-8y=9
-4x+9y=-22

Answers

Answer:

Solution: (1,-2)

Step-by-step explanation:

System of Equations

Given the equations:

[tex]-7x-8y=9\qquad\qquad [1][/tex]

[tex]-4x+9y=-22\qquad\qquad [2][/tex]

We'll solve it by elimination. It means eliminating one of the variables by equating their coefficients. We select the variable y. To eliminate it, multiply the equation [1] by 9 and the equation[2] by 8:

-63x-72y=81

-32x+72y=-176

Adding up both equations:

-95x=-95

Solving:

x=-95/(-95)=1

x=1

Now to eliminate x and find y, multiply [1] by 4 and [2] by -7:

-28x-32y=36

28x-63y=154

Adding up both equations:

-95y=190

Solving:

y=190 / (-95) = -2

y=-2

Solution: (1,-2)

​The radius of the circle shown below is 3 inches.
​What is the area of this circle, in square inches?
​​

Answers

Answer:Multiply Pi (3.1416) with the square of the radius (r) 2. The radius can be any measurement of length. This calculates the area as square units of the length used in the radius. Calculated out this gives an area of 28.2744 Square Inches.

Step-by-step explanation:i hope this helps

Please someone help please hurry ??????

Answers

You need a graph to do that

Kellie is dlowed to watch up
to 90 minutes of TV per day.
If she watched 10 minutes
before school, how many 20-
minute TV episodes can she
watch after school?

Answers

90 min per day

10 min before school

=> she can watch TV during (90-10) 80 minutes after school

if each episode = 20 minutes

she will be able to watch 80:20 soit 4 episodes after school

PLEASE HELP WILL MARK BRAINLIEST
Study the data and answer the question that follows.
July`:
New-35
Used-62
August:
New-45
Used-42
September:
New-20
Used-55
October:
New-27
Used-39
November:
New-51
Used-12
December:
New-38
Used-87

Which type of car had the largest range in monthly sales? Explain how you came up with your answer. PLEASE NO LINKS OR I WILL REPORT YOU

Answers

Answer: hi! December

Step-by-step explanation:

I added all the sails and now my concussion is  December. Please mark branleyest! =^.^=

C, D OR E PLEASE
help I will crown brainliest!!!!

Answers

Answer:

Step-by-step explanation:

c.  y = (x^2 + 3)(x + 4)

y = x^3 + 4x^2 + 3x + 12

d. y = (x^2 + x) / √x

y =   (x^2 + x) /  x^1/2

y = x^2/ x^1/2  +  x / x^1/2

y = x^(2 - 1/2) + x(1 - 1/2)

y = x^3/2 + x^1/2

or x =  √(x^3) + √x

e.   y = 5 /x^2

y = 5x^(-2)

A triangle is rotated 90° about the origin. Which rule describes the transformarion?​

Answers

Answer:

its either counterclockwise or clockwise 90 degree rotation

Step-by-step explanation:

each point of the given figure has to be changed from (x, y) to (y, -x)

.
Which expression is equivalent to (73)−2? (4 points)

1 over 7
1 over 7 times 7 times 7 times 7 times 7 times 7
negative 1 over 7 times 7 times 7 times 7 times 7 times 7
7

Answers

Answer:

The Answer is 1 over 7 times 7 times 7 times 7 times 7 times 7

Step-by-step explanation:

All you have to do is multiply the exponents.

[tex]7^{3*(-2)} =7^{-6}[/tex]

and the rule says :

[tex]x^{-a} = \frac{1}{x^{a} }[/tex]

So that means :

[tex]7^{-6} =\frac{1}{7^{6} } =\frac{1}{7*7*7*7*7*7}[/tex]

hope it helps ... have a good day

1 over 7 times 7 times 7 times 7 times 7 times 7  is equivalent to (73)−2.

What is  multiplication?

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

Here we have,

(7^3)(−2)

=7^(-6)

=1/7^6

=1/7*7*7*7*7*7

Hence, 1 over 7 times 7 times 7 times 7 times 7 times 7  is equivalent to (73)−2.

To learn more on multiplication click:

brainly.com/question/5992872

#SPJ2

if coordinates of midpoint joining the points( -8,13 )and( x ,7) is( 4,10) then value of x is​

Answers

16 because you have to go 12 units from -8 to 4, so you go 12 from 4 and get 16

DO THIS FACTORISATION WITH STEPS!!! 4ax-3bx-8ay+6by

Answers

Step-by-step explanation:

x•(4a-3b)-2y•(4a-3b)

(x-2y)•(4a-3b)

Answer:

Step-by-step explanation:

4ax-3bx-8ay+6by

4ax-x-3bx-x-8ay+6by

4a-3b-2x-8ay+6by

4a-3b-2x-8ay+6by

4a-3b-b-2x-8ay+6b-by

4a-4b-2x-8ay+6y

4a+a-4b-2x-8a+ay+6y

5a-4b-2x-8y+6y

5a-4b-2x-2y

You find a pair of jeans on a clearance rack that originally cost $64. They were marked down 50%. The clearance price sign says an additional 50% off. Johnny says that you do not need to pay anything for the jeans. Do you agree? Why or Why not? Make sure that your answer is given with at least four sentences.

Answers

Answer and explanation:

Original cost of jeans =$64

Markdown by 50%= 0.50*64= $32

Additional discount by clearance sign 50% =0.50*32= $16

Therefore I disagree with Johnny. First the original price $64 was reduced by half of the price 50% of $64 =$32. Secondly the new price $32 is then also reduced by half of it 50% giving us $16. Therefore the discounts did not wipe off all the price as suggested by Johnny.

Assume the following angle is in standard position. Find a positive and negative angle whose absolute value is
less than 360° and is coterminal with the given angle. -485°

Answers

Answer:

Step-by-step explanation:

Negative angle: -485+360=-125 degrees

Positive angle: -485+720=235 degrees

please help ASAP!!! (75 points!!!)

Answers

Answer:

Image its not loading my man, try to re-upload it

Step-by-step explanation:

Write the coordinates of the vertices after a translation 4 units left.

Answers

Answer:

Step-by-step explanation:

what is 1 5/12 + 1 8/12 for iready

Answers

Answer:

3 1/12

Step-by-step explanation:

Originally a rectangle was twice as long as it was wide. When 4 m were added to its length and and 3 m subtracted
from its width, the resulting rectangle has an area of 600 m². Find the dimensions of the new rectangle.

Answers

Answer:

Step-by-step explanation:

Original rectangle

L = 2*w

w = w

New rectangle

2w + 4

w - 3

Area New rectangle

(2w + 4)(w - 3) = 600               Remove the brackets

2w^2 - 6w + 4w - 12 = 600     Combine the left

2w^2 - 2w -  12 = 600             Subtract 600 from both sides

2w^2 - 2w - 600 - 12 = 0        Combine

2w^2 - 2w - 612 = 0                This factors.

(w- 18)(w + 17) = 0

w +  17 will produce nothing useful. What is - 17 m ? Can you measure it?

w = 18

check

Original Triangle

w = 18

L = 36

Derived Triangle

L = 36 + 4 = 40

w = 18 - 3 = 15

LW = 600

Answer

L = 40W = 15

pls help me thx very desparate

Answers

Answer:

4) Dmytro drank more juice

5) Henrietta is older

Step-by-step explanation:

4)

Dmytro drank 7/4 bottles which is 1.75 bottles

Jitka drank 1 1/2 bottles which is 1.5 bottles

So, Dmytro drank more juice

5)

Henrietta is 7 2/3 years old which is 7.66

Jagdeep is 65/12 years old which is 5.41

So, Henrietta is older

100 POINTS!!!

What is the rate of change of the following table?

EXPLAIN

Answers

Answer:

4

I think it is 4

Find the area of the figure.
area
units2

Answers

Answer:

[tex]33 units^{2}[/tex]

I counted the squares.

If f(x) = x^3, find x if f(x) = 1000

help!!

Answers

Answer:

x = 10

Step-by-step explanation:

[tex]\mathsf{given \ f(x)=x^3 \ and \ f(x)=1000}\\\\\mathsf{\implies x^3=1000}\\\\\mathsf{\implies x=\sqrt[3]{1000}}\\\\\mathsf{\implies x=10}[/tex]

get Money for answering this :)

Answers

Answer:

2

Step-by-step explanation:

hope it helps

I agree with 2. Absolutely right ;)

-2k+13=-8k-35
What’s k

Answers

Answer:

k = -8

Step-by-step explanation:

-2k+13=-8k-35

Add 8k to each side

-2k+8k+13=-8k+8k-35

6k +13 = -35

Subtract 13 from each side

6k+13-13 = -35-13

6k = -48

Divide by 6

6k/6 = -48/6

k = -8

An expression is shown below.

Which expression is an equivalent expression?

Please work it out to show how you got the answer.

Answers

Answer:

C

Step-by-step explanation (A):

[tex]\frac{4}{5}(3x+5y)[/tex]

Apply the Distributive Property

[tex]\frac{4}{5}\times3x+\frac{4}{5}\times5y[/tex]

Cross out the common factor

[tex]\frac{4}{5}\times3x+4y[/tex]

Multiply the monomials

[tex]\frac{12}{5}x+4y[/tex]

Determine true/false

[tex]Determine\ whether\ \frac{12}{5}x+\frac{20}{3}y\ and\\ \frac{4}{5}(3x+5y)\ are\ equivalent\\ False[/tex]

Step-by-step explanation (B):

[tex]\frac{4}{15}(3x-5y)[/tex]

Apply the Distributive Property

[tex]\frac{4}{15}\times3x-\frac{4}{15}\times5y[/tex]

Cross out the common factor

[tex]\frac{4}{5}x-\frac{4}{15}\times5y\\ \frac{4}{5}\times-\frac{4}{3}y[/tex]

Determine true/false

[tex]Determine\ whether\ \frac{12}{5}x+\frac{20}{3}y\ and\ \frac{4}{15}(3x-5y)\ are\ equivalent:[/tex]

[tex]False[/tex]

Step-by-step explanation (C):

[tex]\frac{4}{15}(9x+25y)[/tex]

Apply the Distributive Property

[tex]\frac{4}{15}\times9x+\frac{4}{15}\times25y[/tex]

Cross out the common factor

[tex]\frac{4}{5}\times3x+\frac{4}{15}\times25y\\ \frac{4}{5}\times3x+\frac{4}{3}\times5y[/tex]

Multiply the monomials

[tex]\frac{12}{5}x+\frac{4}{3}\times5y\\ \frac{12}{5}x+\frac{20}{3}y[/tex]

Determine true/false

[tex]Determine\ whether\ \frac{12}{5}x+\frac{20}{3}y\ and\ \frac{4}{15}(9x+25y)\ are\ equivalent:\\ True[/tex]

Step-by-step explanation (D):

[tex]\frac{4}{3}(3x-5y)[/tex]

Apply the Distributive Property

[tex]\frac{4}{3}\times3x-\frac{4}{3}\times5y[/tex]

Cross out the common factor

[tex]4x-\frac{4}{3}\times5y[/tex]

Multiply the monomials

[tex]4x-\frac{20}{3}y[/tex]

Determine true/false

[tex]Determine\ whether\ \frac{12}{5}x+\frac{20}{3}y\ and\ \frac{4}{3}(3x-5y)\ are\ equivalent:\\ False[/tex]

I hope this helps you

:)

Bag contains 11 counters. 5 are white
a counter is taken out and not replaced. Second one is taken out. Prob that one of them is white

Answers

Answer:

6/11

Step-by-step explanation:

After taking 2 counters with no replacement, that only one of these is white. We will see that the probability is 6/11.

Given that;

there are 11 counters, 5 of them are white, 6 are not white

First we take the white one, the probability is equal to the quotient between the number of white counters and the total number of counters, so we have:

p = 5/11

And, also notice that there are 2 permutations:

first white, then non-white.

first non-white, then white.

So we need to add a factor 2.

P = 2*p*q = 2*(5/11)*(6/10) = 6/11

The probability is 6/11

We can also Do:

11/11 = Whole

11 - 5 = 6

Hence, Answer = 6/11

~Learn with Lenvy~

From a standard deck of cards, calculate the probability of drawing a queen of hearts. Pls add formula to get to the conclusion

Answers

Answer:

1/52

Step-by-step explanation:

only one queen in a deck of cards

1/52

also the formula is

possibility of getting the outcome/total possible outcomes

Question 5 (5 points)
(02.05 LC)
Which sequence of transformations creates a similar but not congruent triangle? (5 points)
a
Dilation and reflection
b
Reflection and rotation
с
Reflection and translation
d
Translation and rotation

Answers

A
because a dilation changes the size of the shape, but it’s still similar because it’s proportional to the original triangle.

Answer:

A

Step-by-step explanation:

dilation and rotation

Find the equation of the exponential function represented by the table below:

Answers

Answer:

y=a(b)^x

y=0.01(3)^x

a is start, b is multiplier

Estimate the following limit numerically.

limx→2x+3−2x−1

Answers

Answer:

Your answer is 0

Have a great day!

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