1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
VMariaS [17]
3 years ago
5

What are the domain and range of f (x) = log (x minus 1) 2?.

Mathematics
1 answer:
statuscvo [17]3 years ago
8 0

You can use the definition of logarithm and the fact that a positive number raised to any power will always stay bigger than 0.

The domain of the given function is  {x | x > 1 and a real number }

The range of the given function is \mathbb R (set of real numbers)

<h3>What is the definition of logarithm?</h3>

If a is raised to power b is resulted as c, then we can rewrite it that b equals to the logarithm of c with base a.

Or, symbolically:

a^b =  c \implies b = log_a(c)

Since c was the result of a raised to power b, thus, if a was a positive number, then a raised to any power won't go less or equal to zero, thus making c > 0

<h3>How to use this definition to find the domain and range of given function?</h3>

Since log(x-1) is with base 10 (when base of log isn't specified, it is assumed to be with base 10) (when log is written ln, it is log with base e =2.71828.... ) thus, we have a = 10 > 0 thus the input x-1 > 0 too.

Or we have:

x > 1 as the restriction.

Thus domain of the given function is {x | x > 1 and a real number }

Now from domain, we have:

x >  1\\&#10;x-1 > 0\\&#10;log(x-1) > -\infty\\&#10;log(x-1) + 2 > -\infty\\&#10;f(x) > -\infty (log(x-1) > -infinity since log(0) on right side have arbitrary negatively large value which is denoted by -infinity)

Thus, range of given function  is whole real number set \mathbb R (since all finite real numbers are bigger than negative infinity)

Thus, the domain of the given function is  {x | x > 1 and a real number }

The range of the given function is \mathbb R (set of real numbers

Learn more about domain and range here:

brainly.com/question/12208715

You might be interested in
What is the rule for the following sequence: 2, 9, 21, 65
Helga [31]

There is no common ratio or common difference. The first three terms increases more slowly than a cubic, but the last three increase more quickly than the cube of n. The pattern is not obvious to me. When the sequence is cast in recursive terms, you get

... a[n] = (48/13)a[n-2] + (59/39)a[n-1] . . . . a[1] = 2, a[2] = 9

The next term using this rule is 174 34/39, not an integer.

The coefficients p and q for a[n-2] and a[n-1] can be found from

2p+9q=21\\9p+21q=65

_____

Any sequence of 4 numbers can be matched by a polynomial of degree 3 or less. Here, a calculator's polynomial regression function tells us the rule could be

... a[n] = 4.5n³ -24.5n² +49n -27

Using this rule, the next two terms are 168 and 357.

5 0
3 years ago
Help me please! I’m begging
Goryan [66]

12) the radius is 15 so with the equation (3.14)*r^2, we get (3.14)(15^2)=706.5

13) true, true (if x=4), true

14) y=0.75x+4.50, $8.25

7 0
3 years ago
I have to put spaces so delete the spaces ok
loris [4]

Answer:

wdym???

Step-by-step explanation:

You have an email with  at white buffalos.net??? I thought that was only my school.

3 0
3 years ago
In the diagram below, TUVW is a rectangle. Prove triangle TZW is congruent to triangle UZV.
otez555 [7]

Answer:

By S.S.S. congruence property;  ΔTZW ≅ ΔVZU

Step-by-step explanation:

Given:

TUVW is a rectangle.

To Prove : TZW ≅ UZV

Proof:

Since TUVW is a rectangle, and we know that opposite side of a rectangle is equal.

So,

TW = UV \ \ .\ .\ .\ .\ 1

And also TV and WU are the diagonals of the rectangle.

And the diagonals of rectangle bisects each other.

Therefore;

TZ=ZV.........\ 2\\\\WZ=ZU..........\ 3

Now In ΔTZW and ΔVZU

TW = UV (from 1)

TZ = ZV (from 2)

WZ = ZU (from 3)

So, by S.S.S. congruence property;

ΔTZW ≅ ΔVZU

Hence proved.

8 0
3 years ago
I want to be challenged more, so could anyone give me some 4th grade math problems​
nexus9112 [7]

I'm in 7th grade u want those math problems???

6 0
3 years ago
Read 2 more answers
Other questions:
  • When flying a kite Peter without 45 feet of string and anchors it to the ground. He determines the angle of elevation of the kit
    13·1 answer
  • The weight of a rock sample is measured to be 2.5 ponds. What is the percent of error in the measurement?
    6·1 answer
  • Mack is repackaging 6/8- pound bags of birdseed into 1-pound bags of birdseed.What is the least number of 6/8 -pound bags of bir
    14·2 answers
  • A and B can do a piece of work in 30 days, while B and C can do the same work in 24 days and C and A in 20 days. If they all wor
    15·1 answer
  • .
    8·1 answer
  • The ratio of dogs to cats in a veterinarian's office is 9:7. What is the ratio of the number of dogs
    9·1 answer
  • (9x – 9)<br> (3x + 9)°/B<br> Find the measure of ABC
    15·1 answer
  • Lola already has 6 pennies, and she plans to save more. In her first week
    14·1 answer
  • 1.5 cm 1 30 cm 15 cm 20 cm Calculate the volume of the box using the external measurements.​
    6·1 answer
  • A rectangular pen has a length 4 feet greater than its width. Find the area
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!