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
Natali5045456 [20]
1 year ago
14

Determine the domain and range Express your answer in interval notation

Mathematics
1 answer:
Dmitriy789 [7]1 year ago
7 0

The domain of a function is the set of all values that the x-variable can take.

On the other hand, the range of the function is the set of all values that the function takes when it is evaluated at elements of the domain.

For the given expression:

p(x)=-\frac{1}{(x-1)^2}

The denominator is (x-1)^2. Since the denominator must be different from 0, then:

\begin{gathered} (x-1)^2\ne0 \\ \Rightarrow x-1\ne0 \\ \Rightarrow x\ne1 \end{gathered}

Then, the only restriction for the variable x is not to be equal to 1. Then, the domain of p(x) is the set of all real numbers except 1, which can be written using interval notation as:

(-\infty,1)\cup(1,\infty)

Since the exponent of the denominator is 2, then the denominator is always positive. Since the coefficient of the term 1/(x-1)^2 is -1, then the whole expression must always be negative. Additionally, there is no way in which the expression can be equal to 0.

Then, the range of the function is the set of all negative numbers, which can be expressed using interval notation as:

(-\infty,0)

Therefore, the answers are:

\begin{gathered} \text{ Domain: }(-\infty,1)\cup(1,\infty) \\  \\ \text{ Range: }(-\infty,0) \end{gathered}

You might be interested in
Which of the following is equal to [(x2y3)-2/(x6y3x)2]3 ?
Alona [7]

Answer:

a=√x3y5 or a=−√x3y5

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
Can you answer this for me plssss 0.5(r+2.75)=3
lora16 [44]

Step-by-step explanation:

0.5 ( r + 2.75 ) = 3

r + 2.75 = 3 / 0.5

r + 2.75 = 6

r = 6 - 2.75

r = 3.25

4 0
3 years ago
Read 2 more answers
The formula K=C+273.15 converts temperatures from Celsius C to Kelvin K.
Vanyuwa [196]
A. C= K-273.15
b. 300= C+273.15
300-273.15= C
26.85=C
4 0
3 years ago
What is 2-2 equals to ?
Nikitich [7]

Answer:

The answer is 0

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
Which expression is equivalent to w4−25w2+144
eduard
Sorry I’m just commenting to do it
8 0
3 years ago
Other questions:
  • How do you solve for tan-1 or tan theta without using a calculator? I don't want to rely on the calculator to solve problems tha
    15·1 answer
  • Kristen has 64 coins in her piggy bank. she has $9.25 in dimes and quarters. how many dimes and quarters does she have.
    12·1 answer
  • Please help me on this asap this is very important :D
    13·1 answer
  • If cos(theta)= the square root of 3 divided by 2 then what what does cos squared theta =
    9·1 answer
  • The regular cost of a sound system is $1499, but today it is on sale for $1100! That is a $399 saving. The sales clerk tells you
    5·1 answer
  • If you made 12 pies and each one has 1 cup of sugar how many cups will you need to make 27 pies
    12·2 answers
  • Tina is taking picture of her friends. if she sets a tripod level on the ground, will the bottom of each of the legs of tripod b
    5·1 answer
  • Please help me ... I neddddd helpppp.
    9·1 answer
  • HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP FASTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTT
    9·2 answers
  • Help plis! Someone I need help with this plis
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!