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
soldier1979 [14.2K]
3 years ago
12

Choose the domain for which each function is defined

Mathematics
1 answer:
klemol [59]3 years ago
6 0

Answer:

Part 1) f(x)=\frac{x+4}{x} -----> x\neq 0

Part 2) f(x)=\frac{x}{x+4} ----> x\neq -4

Part 3)  f(x)=x(x+4) ----> All real numbers

Part 4) f(x)=\frac{4}{x^2+8x+16} ----> x\neq -4

Step-by-step explanation:

we know that

The domain of a function is the set of all possible values of x

Part 1) we have

f(x)=\frac{x+4}{x}

we know that

In a quotient the denominator cannot be equal to zero

so

For the value of x=0 the function is not defined

therefore

The domain is

x\neq 0

Part 2) we have

f(x)=\frac{x}{x+4}

we know that

In a quotient the denominator cannot be equal to zero

so

For the value of x=-4 the function is not defined

therefore

The domain is

x\neq -4

Part 3) we have

f(x)=x(x+4)

Applying the distributive property

f*(x)=x^2+4x

This is a vertical parabola open upward

The function is defined by all the values of x

therefore

The domain is all real numbers

Part 4) we have

f(x)=\frac{4}{x^2+8x+16}

we know that

In a quotient the denominator cannot be equal to zero

so

Equate the denominator to zero

x^2+8x+16=0

Remember that

x^2+8x+16=(x+4)^2

(x+4)^2=0

The solution is x=-4

so

For the value of x=-4 the function is not defined

therefore

The domain is

x\neq -4

You might be interested in
2 (5y-4)&gt;32<br> Solve the inequality for y.
scoray [572]

Answer:

y > 4

Step-by-step explanation:

2 (5y-4)>32

Divide each side by 2

2/2 (5y-4)>32/2

5y-4 > 16

Add 4 to each side

5y-4+4 > 16+4

5y > 20

Divide each side by 5

5y/5 > 20/5

y > 4

5 0
3 years ago
Read 2 more answers
Jacob decided to ride his bicycle across the country during his 2-month summer vacation. the route he took from washington, dc t
Artist 52 [7]

Step 1: Assign variable for the unknown that we need to find.

Let ' x ' be the number of miles traveled by Jacob so far (His distance from starting point)

Step 2: Use the sentence given to set up an equation

Sentence 1: "His distance from his starting point was exactly 100 miles more than three times the distance remaining until the finishing point"

Total distance is 2800 miles, if his distance from the starting point is 'x', then remaining distance can be represented by 2800 - x.

Using the sentence we can write the below equation...

x = 100 + 3(2800 - x)

Distributing 3 in the right side of the equation, we get...

x = 100 + 8400 - 3x

Adding 3x on both sides of the equation, we get...

x+3x = 8500

Combine like terms in the left side of the equation, we get...

4x=8500

Dividing 4 on both sides of the equation, we get...

\frac{4x}{4} =\frac{8500}{4}

Simplifying the fraction on either side of the equation, we get...

x=2125miles

Conclusion:

Out of the 2800 miles, Jacob travelled a distance of 2125 miles and remaining miles that he need to cover will be <u>675 miles</u>.

3 0
3 years ago
Alex purchased a new car for $28,000. The car's value depreciates 7.25% each year. What will be the value of the car 5 years aft
Anestetic [448]
A = 28000(0.9275)^5

a = 19219

$19,219 is the answer

Hoped this helped 
8 0
3 years ago
What is the answer to this question?
Elena-2011 [213]
Where’s the question-
3 0
3 years ago
Can someone please help me?
Luda [366]

Answer:

(x-1)^5 (x+1)

Step-by-step explanation:

2 (x-1)^5 + (x-1)^6

Factor out (x-1)^5

2 (x-1)^5 + (x-1)^5 (x-1)

(x-1)^5( 2 + x-1)

Combine like terms

(x-1)^5 (x+1)

4 0
2 years ago
Read 2 more answers
Other questions:
  • How many water glasses are in a 17oz bottle?
    10·1 answer
  • To estimate a population mean, the sample size needed to provide a margin of error of 3 or less with a 95% confidence when the p
    9·1 answer
  • Mustafa’s soccer team is planning a school dance as a fundraiser. The DJ charges $200 and decorations cost $100. The team decide
    11·2 answers
  • What is the answer to 1/3 ✖9
    14·2 answers
  • What is 12A =-19 plz help
    8·1 answer
  • In Triangle EFG,9 = 12 inches, e = 55 inches and Angle F=75º. Find the area of Triangle EFG, to the
    10·1 answer
  • Help meeeeeeeeeeeeeeeeeeeee
    11·1 answer
  • Help me with this please
    6·1 answer
  • 5. Using the information from a previous problem and given the tax table, find
    10·1 answer
  • X
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!