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
MrRissso [65]
3 years ago
6

Determine the domain of the function (fog)(x) where f(x)=3x-1/x-4 and g(x)=x+1/x

Mathematics
1 answer:
Katarina [22]3 years ago
5 0

Answer: (-∞,-1) ∪ (0,+∞)

Step-by-step explanation: The representation fog(x) is a representation of composite function, meaning one depends on the other.

In this case, fog(x) means:

fog(x) = f(g(x))

fog(x) = 3(x+\frac{1}{x} )-\frac{1}{x+\frac{1}{x} } -4

fog(x)=3x+\frac{3}{x} -\frac{1}{\frac{x^{2}+x}{x} } -4

fog(x)=3x+\frac{3}{x} -\frac{x}{x^{2}+x} -4

fog(x)=\frac{3x^{2}(x^{2}+x)+3(x^{2}+x)-x-4x(x^{2}+x)}{x(x^{2}+x)}

fog(x)=\frac{3x^{4}+3x^{3}+3x^{2}+3x-x-4x^{3}+4x^{2}}{x(x^{2}+x)}

fog(x)=\frac{3x^{4}-x^{3}-x^{2}+2x}{x(x^{2}+x)}

This is the function fog(x).

The domain of a function is all the values the independent variable can assume.

For fog(x), denominator can be zero, so:

x(x^{2}+x) \neq 0

If x = 0, the function doesn't exist.

x^{2}+x \neq0

x(x+1) \neq0

x+1\neq0

x\neq-1

<u>Therefore, the domain of this function is: </u><u>-∞ < -1 or x > 0</u>

You might be interested in
I need help ASAP please
Vilka [71]

Answer:A -3,6

Step-by-step explanation: Substitue the answers in and they work out

3 0
3 years ago
A simple random sample of 36 men from a normally distributed population results in a standard deviation of 10.1 beats per minute
Katyanochek1 [597]

Answer:

Step-by-step explanation:

Given that:

sample size n = 36

standard deviation = 10.1

level of significance ∝ = 0.10

The null hypothesis and the alternative hypothesis can be computed as follows:

H_0 : \sigma = 10

H_1 : \sigma \neq 10

The test statistics can be computed as follows:

X^2 = \dfrac{(n -1)s^2 }{\sigma ^2}

X^2 = \dfrac{(36 -1)10.1^2 }{10^2}

X^2 = \dfrac{(35)102.01 }{100}

X^2 = \dfrac{3570.35 }{100}

X^2 =35.704

degree of freedom = n - 1 = 36 - 1 = 35

Since this test is two tailed .

The P -value can be determined by using the EXCEL FUNCTION ( = 2 × CHIDIST(35.7035, 35)

P - value = 2 × 0.435163515

P - value = 0.8703      ( to four decimal places)

Decision Rule : To reject the null hypothesis if  P - value is less than the 0.10

Conclusion: We fail to reject null hypothesis ( accept null hypothesis) since p-value is greater than 0.10 and we conclude that there is sufficient claim that the normal range of pulse rates of adults given as 60 to 100 beats per minute resulted to a standard deviation of 10 beats per minute.

3 0
3 years ago
Solve the equation by expressing each side as a power of the same base and then equating exponents.
Kitty [74]
I hope this helps. If I need to know explain further let me know.

3 0
3 years ago
Read 2 more answers
He following formula is used in economics to find a factory's unit labor cost UUU, where OOO is the hourly output per worker and
Vilka [71]

Answer:

W = O/U

Step-by-step explanation:

U/1 = O/W

WU=O

W = O/U

4 0
2 years ago
Math help (Tan) + brainy
levacccp [35]
Tan = opposite / adjacent
tan 74 = 24/7

6 0
3 years ago
Read 2 more answers
Other questions:
  • Solve this equation<br> y= 2x<br> x= -y + 6
    15·1 answer
  • Factor out GCF 25x^7 + 45x^3
    7·1 answer
  • Multiply (2.4 ⋅ 1014) ⋅ (4 ⋅ 107). Express the answer in scientific notation.
    15·2 answers
  • Which points lie on the line y = 3x - 7?
    6·1 answer
  • 5/12+3/5= what's the answer
    12·1 answer
  • which uppercase letters will not appear reversed when they are held in front of a mirror? what type of symmetry do these letters
    8·1 answer
  • Solving Exponential Equations (lacking a common base) <br> Solve the exponential equation 6u = 22
    14·2 answers
  • The next model of a sports car will cost 11.2% less than the current model. The current model costs $36,000. How much will the p
    10·1 answer
  • Which of the following statements describes a correct method for solving the equation below?
    9·1 answer
  • ?????????????????????????????????????????????????????
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!