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
kherson [118]
2 years ago
6

The functions $f$ and $g$ are defined as follows: \[f(x) = \sqrt{\dfrac{x+1}{x-1}}\quad\text{and}\quad g(x) = \dfrac{\sqrt{x+1}}

{\sqrt{x-1}}. \]explain why the functions $f$ and $g$ are not the same function.
SAT
1 answer:
AlladinOne [14]2 years ago
4 0

Recall that √x has a domain of x ≥ 0.

So, f(x) is defined as long as

(x + 1)/(x - 1) ≥ 0

• We have equality when x = -1

• Otherwise (x + 1)/(x - 1) is positive if both x + 1 and x - 1 are positive, or both are negative:

\begin{cases}x+1>0 \implies x>-1 \\ x-1>0 \implies x>1\end{cases} \implies x > 1

\begin{cases}x+1

Then the domain of f(x) is

x > 1   or   x ≤ -1

On the other hand, g(x) is defined by two individual square root expressions with respective domains of

• x + 1 ≥ 0   ⇒   x ≥ -1

• x - 1 ≥ 0   ⇒   x ≥ 1

but note that g(1) is undefined, so we omit it from the second domain.

Then g(x) is defined so long as both x ≥ -1 *and* x > 1 are satisfied, which means its domain is

x > 1

f(x) and g(x) have different domains, so they are not the same function.

You might be interested in
Carefully examine the impact of drug addiction on emotional and physical wellbeing
viva [34]
I can personally say it changes your life & others around you. It will constantly make you have irrational thoughts and you won’t have a clear head space. Personally watching family go through that it’s never easy
8 0
3 years ago
If you were trapped on a desert island with no source of fresh water should you drink water from the ocean
kykrilka [37]

Answer:

no

Explanation:

the ocean has salt water which isn't good for you

8 0
2 years ago
Read 2 more answers
The melody in this excerpt is played by a trombone.
Lera25 [3.4K]

Based on the excerpt from the contemporary composer Aulis Sallinen, the melody is played by a trombone: False.

<h3>What is an inference?</h3>

An inference refers to a process through which a reader or listener can deduce the meaning or message (information) such as melody, that's associated with an event or musical composition, especially through induction.

Based on the excerpt from the contemporary composer Aulis Sallinen, we can infer and logically deduce that the melody is played by a flute, rather than a trombone.

Read more on flute here: brainly.com/question/1173149

#SPJ1

5 0
2 years ago
Which of the following are true about the Medicare Access and CHIP Reauthorization Act of 2015 (MACRA) Plans and the impact to P
devlian [24]

The true statement about the Medicare Access and CHIP Reauthorization Act of 2015 (MACRA) Plans and the impact to Plans C and F are:

  1. "Consumers eligible for Medicare Part A on or after January 1, 2020,will not be able to purchase Medicare Supplement Insurance Plans C or F."
  2. "Consumers eligible for Medicare Part A before January 1 2020 can enroll in Plan C or F even after 2020 and can keep their plans as long as they choose."

<h3>What is MACRA?</h3>

MACRA is an abbreviation for Medicare Access and CHIP Reauthorization Act of 2015 and it can be defined as a bipartisan United States statute (legislation) that was signed into law on the 16th of April, 2015, so as to change how the federal government pay physicians in the United States of America.

Based on the Medicare Access and CHIP Reauthorization Act of 2015 (MACRA) Plans, the impact to Plans C and F include the following:

  1. "Consumers eligible for Medicare Part A on or after January 1, 2020,will not be able to purchase Medicare Supplement Insurance Plans C or F."
  2. "Consumers eligible for Medicare Part A before January 1 2020 can enroll in Plan C or F even after 2020 and can keep their plans as long as they choose."

Read more on MACRA here: brainly.com/question/28045174

#SPJ1

3 0
2 years ago
Butterflies usually are identified by the colors and patterns on their wings. Butterflies have four wings: the two wings near th
netineya [11]

The species of butterfly that is shown is; Papilio polyxenes.

<h3>What are the species of butterflies?</h3>

Butterflies usually are identified by the colors and patterns shown on their wings. However, for us to identify an organism using a dichotomous key, we must compare the traits of the organism to the first pair of descriptive statements on the key as follows;

1) A swallowtail butterfly is either classified as Papilio glaucus ( where the wings are mainly yellow) or Papilio polyxenes(where the wings are mainly black)

Now, the image of the butterfly given shows that the wings are mainly black, and as a result, we will say that the butterfly specie is called Papilio Polyxenes.

Read more about species of butterflies at; brainly.com/question/16678828

6 0
2 years ago
Other questions:
  • Which of the following is a tip for taking the aspire reading test
    11·2 answers
  • What are the two principal ways to relieve test anxiety??????
    6·2 answers
  • Which of the following does not influence the rate of weathering of rock?
    6·2 answers
  • Help me please with this
    6·2 answers
  • What is the best type of cheese.
    6·1 answer
  • How do i get my out of my but
    10·1 answer
  • What is your theme for your story? (one sentence)*
    13·1 answer
  • In order to buy a house, a couple takes a mortgage of M dollars at an annuel rate of r percent to be paid off over N months
    13·1 answer
  • Diego made 6 boxes of spaghetti to feed the 20 people who attended his dinner party. Next time, 50 people are coming! how many b
    5·1 answer
  • How does the cartoonist use exaggeration in this cartoon to create meaning.
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!