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Snezhnost [94]
3 years ago
12

What is the domain of the function f(x) =x+1/ X^2-6x+8?

Mathematics
1 answer:
SpyIntel [72]3 years ago
8 0

Answer:

The domain of the function is all real values of x, except x = 4 and x = 2

Step-by-step explanation:

We are given the following function:

f(x) = \frac{x+1}{x^2-6x+8}

It's a fraction, so the domain is all the real values except those in which the denominator is 0.

Denominator:

Quadratic equation with a = 1, b = -6, c = 8

Using bhaskara, the denominator is 0 for these following values of x:

\Delta = (-6)^2 - 4(1)(8) = 36-32 = 4

x_{1} = \frac{-(-6) + \sqrt{4}}{2} = 4

x_{2} = \frac{-(-6) - \sqrt{4}}{2} = 2

The domain of the function is all real values of x, except x = 4 and x = 2

You might be interested in
15. 3x – 4y = -1<br> 5x + 2y = 7
never [62]

Answer:

x = 1, y = 1

Step-by-step explanation:

3x - 4y = -1

5x + 2y = 7

If we multiply the whole second equation by 2, we get:

10x + 4y = 14

Adding this to the first equation:

10x + 4y + 3x - 4y = 14 - 1

13x = 13

x = 1

Applying this to the second equation:

5 (1) + 2y = 7

2y = 2

y = 1

8 0
3 years ago
CONSTRUCTION Carlos is building a screen door. The height of the door is I foot more than twice its width. What is the width of
-BARSIC- [3]

Answer:

<h2>width = 3 feet</h2>

Step-by-step explanation:

Let h be the height of the door

and w be its width

The statement “The height of the door is I foot more than twice its width”

can be translated mathematically like this :  h = 2w + 1

Let’s solve the equation for w:

h = 2w + 1

⇔ 2w = h - 1

\Leftrightarrow w=\frac{h-1}{2}

now , if the door is 7 feet high then it’s width is equal to :

\Rightarrow \frac{7-1}{2} =\frac{6}{2} =3 \ ft

6 0
1 year ago
Read 2 more answers
Help me ples!!!!!!!!!!!!!!!!!
bearhunter [10]
It would be subtraction I think
6 0
3 years ago
The Johnson twins were born five years after their older sister. This​ year, the product of the three​ siblings' ages is exactly
Mamont248 [21]

Answer:

13 years.

Step-by-step explanation:

Suppose, today, the Johnson twins' age is x years. Then the age of their elder sister will be (x + 5) years old. It is given that product of the three​ siblings' ages is exactly 2998 more than the sum of their ages. Therefore:

x + x + x + 5 + 2998 = (x)(x)(x + 5).

3x + 3003 = x^3 + 5x^2.

x^3 + 5x^2 - 3x - 3003 = 0.

To solve the question, factor theorem will be used. It states if any number c satisfies the equation f(c) = 0, then c is the factor of f(x). By observation, it can be seen that x = 13 can be a possible candidate for the factor of f(x). To verify, check f(13).

f(13) = 13^3 + 5(13^2) - 3(13) - 3003 = 2197 + 845 - 39 - 3003 = 0.

Since f(13) = 0, therefore x = 13 is the factor of f(x).

Now applying synthetic division:

Column 1       2       3       4            5

     13    |         1       5      -3        -3003  (Row 1)

______|______<u>  _13__234___3003</u>   (Row 2)

            |         1       18      231          0    (Row 3)

The method requires to write the coefficients of all the powers in the Row 1 on the right hand side of the table. Put the factor x = 13 on the left hand side of the table (Row 1 Column 1). The first step involves the second column elements to be added. Since there is only 1, thus there will be 1 below the line. Next step involves multiplying 1 with the factor (which is 13) and this will be the element for row 2 column 3. The add the elements of the column 3. The answer comes out to be -3. Repeat the above steps for the columns 4 and 5. The sum of the column 5 (the last column) should be 0, which is the case. The elements of the last row are actually the coefficients of the quadratic equation which is resultant from dividing f(x) by (x - 13). Thus:

x^2 + 18x + 231 = 0.

Using completing the square:

x^2 + 18 = -231.

(x)^2 + 2*(x)*(9) + (9)^2 = -231 + (9)^2.

(x + 9)^2 = -231 + 81.

(x + 9)^2 = -150.

Taking square root on both sides shows that rest of the 2 answers of this polynomial will be complex roots since square root of -150 does not exist in real numbers. Therefore, since the age is a real quantity and not a complex quantity, the age of the twins is 13 years!!!

8 0
3 years ago
How do you write out in word form 233,740
allsm [11]
The answer is two hundred thirty-three thousand seven hundred forty.
Hope that helped you!
4 0
2 years ago
Read 2 more answers
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