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
Sauron [17]
3 years ago
8

Consider the functions f and g defined by \[f(x) = \sqrt{\dfrac{x+1}{x-1}}\qquad\qquad\text{and}\qquad\qquad g(x) = \dfrac{\sqrt

{x+1}}{\sqrt{x-1}}.\]Explain why f and g are not the same function.
Mathematics
1 answer:
tino4ka555 [31]3 years ago
4 0

Answer:

The given functions are not same because the domain of both functions are different.

Step-by-step explanation:

The given functions are

f(x)= \sqrt{\dfrac{x+1}{x-1}}

g(x) = \dfrac{\sqrt{x+1}}{\sqrt{x-1}}

First find the domain of both functions. Radicand can not be negative.

Domain of f(x):

\dfrac{x+1}{x-1}>0

This is possible if both numerator or denominator are either positive or negative.

Case 1: Both numerator or denominator are positive.

x+1\geq 0\Rightarrow x\geq -1

x-1\geq 0\Rightarrow x\geq 1

So, the function is defined for x≥1.

Case 2: Both numerator or denominator are negative.

x+1\leq 0\Rightarrow x\leq -1

x-1\leq 0\Rightarrow x\leq 1

So, the function is defined for x≤-1.

From case 1 and 2 the domain of the function f(x) is (-∞,-1]∪[1,∞).

Domain of g(x):

x+1\geq 0\Rightarrow x\geq -1

x-1\geq 0\Rightarrow x\geq 1

So, the function is defined for x≥1.

So, domain of g(x) is [1,∞).

Therefore, the given functions are not same because the domain of both functions are different.

You might be interested in
Dot plots are often used for what 2 sets of data
emmainna [20.7K]

Answer:

categorical or quantitative data

Step-by-step explanation:

6 0
3 years ago
Which of the following would be the most logical first step to solving this
Sauron [17]

Answer:

subtract 2 on both sides

5 0
3 years ago
Read 2 more answers
PLEASE HELP!!! WILL GIVE BRAINLIEST AND ITS WORTH 30 points!!
olasank [31]
145*.

Hope this helps
3 0
3 years ago
Read 2 more answers
Jose earns $400 during the summer. He deposits it in an account that pays simple interest at a rate of 3% per year. Which equati
a_sh-v [17]

Answer:

12

Step-by-step explanation:

Since this is simple interest the equation will be P*T*R=I  T=time which is 1 year. P=money invested or borrowed  (aka princable) which is 400$. R=Annual rate is 3% per year and I= Interest after the number of years (aka answer) Hope this helps :)

8 0
3 years ago
Read 2 more answers
Help meeeeee please chile
nasty-shy [4]

Answer:

Step-by-step explanation:

Acute angle

5 0
3 years ago
Read 2 more answers
Other questions:
  • Evaluate the function at the fiven values of the variables:
    8·1 answer
  • Jamal deposits $1000 into a savings account on his 18th birthday. If the 2% interest is compounded yearly, how much will he have
    8·1 answer
  • Kudzu is a vine that grows very fast. Ellie measured one Kudzu vine at 18 3/4 feet. One week later, the vine measure 23 7/8 feet
    8·1 answer
  • Why does the solution for an absolute value equation or inequality typically result in a pair of equations or inequalities?
    11·1 answer
  • What is 372 divided by 6 in estimation
    15·2 answers
  • The value of y varies jointly with x and z. If y = 7 when z = 196 and x = 2, find the value of y when x = 3 and z = 336. I will
    7·1 answer
  • A math test has 12 multiplication problems and 24 division problems.
    5·2 answers
  • Max invests some money in a savings bond.
    10·1 answer
  • Which of these equations are in slope-intercept form?
    15·1 answer
  • DOES THE THE NUMBER LINE GOES ON FORVEVER
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!