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]
2 years ago
5

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

Mathematics
1 answer:
statuscvo [17]2 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
Pretty please for a homie
leonid [27]
Slope is -2
_______
Y+4=-2x+8
Y=-2x+4
3 0
3 years ago
Write an expression that equals 40 include the Exponent
Leokris [45]

Maybe let's just do the prime factorization.

40=2x2x2x5

answer:2^3x5

4 0
3 years ago
HELP NEEDED PLEASE!
tigry1 [53]

Answer:

the answer is about 62

Step-by-step explanation:

3 0
3 years ago
Can somebody give an example of how to identify a polynomial
Nikitich [7]
It has to obey all the polynomial rules, like 3x^4 or 6x, it has to have the base then the power.
4 0
3 years ago
What is a polygon with four right angles and four sides
german

a square ///////////

4 0
3 years ago
Read 2 more answers
Other questions:
  • What is the missing length of the rectangle
    11·1 answer
  • On a piece of paper, graph y = 2x - 4. Then determine which answer matches<br> the graph you drew.
    9·1 answer
  • Find the area of the rectangle. 8 cm 16 cm​
    6·2 answers
  • Which three-dimensional figure is made from the net shown?.Help me​
    8·2 answers
  • In 12 hours , the temperature fell steadily from 17F to -7F. What was the change in temperature
    13·1 answer
  • A certain westbound U.S. highway truck route near a river has a downhill grade of 9%. (a) Explain what a 9% downhill grade means
    12·1 answer
  • Evaluate the expression when a= 4, b= -6, c= -12
    15·2 answers
  • What is a arc, radius, and diameter of a circle?
    8·1 answer
  • Rewrite in simplest terms: -3(s – 10) + 7(-2s – 1)
    11·2 answers
  • I need to get this done, please help
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!