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
Anastasy [175]
3 years ago
8

Explain why f(x) = x2+4/x2-x-2 is not continuous at x = 2.

Mathematics
2 answers:
emmasim [6.3K]3 years ago
7 0

Answer:

Step-by-step explanation:

We have given a function :

f(x) = (x²+4)/(x²-x-2)

We have to explain why the function is not continuous at x = 2.

Simplify the denominator of the function.

x²-x-2 = x²+x-2x-2

x²-x-2 = (x+1)(x-2)

Putting this simplification of denominator in above function we get,

f(x) =  (x²+4)/(x+1)(x-2)

The domain is the all possible values of x in for which the function is defined.

when we put x=2, the denominator is zero and function is undifined.

So, the function is not  continuous at x = 2.

Choice a  is correct.

xxTIMURxx [149]3 years ago
6 0

Answer: Option a.

Step-by-step explanation:

 Make the denominator equal to zero and solve for x:

Factor the quadratic equation. Find two number whose sum is -1 and whose product is -2. Then:

x^{2}-x-2=0\\(x-2)(x+1)=0\\x=2\\x=-1

Then, as you can see the value x=2 makes the denominator equal to zero and the division by zero does not exist. Therefore you can conclude that the function shown in the problem is not defined at x=2

The answer is the option a.

You might be interested in
A road bike has a wheel diameter of 622 mm. What is the circumference of the wheel? Use 3.14 for pi
Ghella [55]

Answer:

Circumference ≅ 195 mm

Step-by-step explanation:

The circumference of a circle is equal to: 2*\pi *radius

Since Diameter = 2*radius we can replace that in the circumference equation giving us:

Circumference = \pi *Diameter

We know Diameter = 622 mm and pi = 3.14 so:

Circumference = \pi *Diameter = 3.14 * 622 mm = 195.308 mm

7 0
3 years ago
Read 2 more answers
What is 3 5/8 ÷14 please answer this
MissTica

Answer:

29/112

Step-by-step explanation:

3 5/8=29/8

(29/8)/14

(29/8)(1/14)=29/112

5 0
3 years ago
What’s the slope of a line that’s perpendicular to y = 2 x + 7
Zina [86]

Answer:The slopw is -1/2

Step-by-step explanation

A slope that is a opposite reciprocal of another slope is always perpendicular. Make sure it is a opposite reciprocal. Not just a regular reciprocal.

8 0
3 years ago
What is 90x10 free brainlest and points
ss7ja [257]

Answer:

900

Step-by-step explanation:

  • 90 * 10
  • 900
8 0
2 years ago
Read 2 more answers
In ANOP, NP is extended through point P to point Q, m_OPQ = (9x – 19)°,
jarptica [38.1K]

Answer:

The values of x and y are x = 6 and y = 9Step-by-step explanation:

MNOP is a parallelogram its diagonal MO and PN intersected at point A

In any parallelogram diagonals:

Bisect each other

Meet each other at their mid-point

In parallelogram MNOP

∵ MO and NP are its diagonal

∵ MO intersect NP at point A

- Point A is the mid-point pf them

∴ MO and NP bisect each other

∴ MA = AO

∴ PA = AN

∵ MA = x + 5

∵ AO = y + 2

- Equate them

∴ x + 5 = y + 2 ⇒ (1)

∵ PA = 3x

∵ AN = 2y

- Equate them

∴ 2y = 3x

- Divide both sides by 2

∴ y = 1.5x ⇒ (2)

Now we have a system of equations to solve it

Substitute y in equation (1) by equation (2)

∴ x + 5 = 1.5x + 2

- Subtract 1.5x from both sides

∴ - 0.5x + 5 = 2

- Subtract 5 from both sides

∴ - 0.5x = -3

- Divide both sides by - 0.5

∴ x = 6

- Substitute the value of x in equation (2) to find y

∵ y = 1.5(6)

∴ y = 9

The values of x and y are x = 6 and y = 9

5 0
2 years ago
Other questions:
  • R is positive can someone simplify it ik it may actually be simple lol
    6·1 answer
  • What are the coordinates (x, y) at which the graphs of 3.6x − 2y = 6 and −2.7x + y = 3 intersect? Round to the nearest tenth if
    8·1 answer
  • If the trapezoid below is reflected across the x-axis, what are the coordinates of B?
    15·2 answers
  • This question is worth 30 points! Look at the image and answer the question.
    12·1 answer
  • I WILL GIVE A LOT OF POINTS AND BRAINLIEST
    13·1 answer
  • Is (1,1) a solution the equation 2x - y = 1 ?​
    15·2 answers
  • ASAP question in the picture
    13·1 answer
  • Simplify 2xy + x²y - 3xy + 4x²y =​
    8·1 answer
  • 4x + 2y = 4<br> Is y a function of x?
    5·1 answer
  • on a particular day, a man spent 12 minutes more driving to his office than driving home. His average speed from home to office
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!