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Natasha2012 [34]
3 years ago
7

Find the domain for the rational function f of x equals quantity x plus 1 end quantity divided by quantity x minus 2 end quantit

y.
(−[infinity], 2) (2, [infinity])

(−[infinity], −2) (−2, [infinity])

(−[infinity], 1) (1, [infinity])

(−[infinity], −1) (−1, [infinity])
Mathematics
1 answer:
Elena L [17]3 years ago
7 0

Answer:

(- \infty, 2), (2, \infty)

Step-by-step explanation:

Given the function:

f(x) = \dfrac{x+1}{x-2}

To find:

Domain of the function.

Solution:

First of all, let us learn about definition of  domain of a function.

Domain of a function is the valid input values that can be provided to the function for which output is defined.

OR

Domain of a function f(x) are the values of x for which the output f(x) is a valid value.

i.e. The function does not tend to \infty or does not have \frac{0}0 form.

So, we will check for the values of x for which f(x) is not defined.

For value to tend to \infty, denominator will be 0.

x-2\neq 0 \\\Rightarrow x \neq 2

So, the domain can not have x = 2

Any other value of x does not have any undefined value for the function f(x).

Hence, the answer is:

\bold{(- \infty, 2), (2, \infty)}     [2 is not included in the domain].

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2 years ago
1. Which point on the axis satisfies the inequality y
grigory [225]

Answer:

1) Point (1,0) -----> see the attached figure N 1

2) The value of x is 4

3) I quadrant

4) (1,1)

5)  y>-5x+3

Step-by-step explanation:

Part 1)

we know that

If the point satisfy the inequality

then

the point must be included in the shaded area

The point (1,0) is included in the shaded area

Part 2)

we have

x-2y\geq 4

see the attached figure N 2

we know that

The value for x on the boundary line and the x axis is equal to the x-intercept of the line x-2y= 4

For y=0

Find the value of x

x-2(0)= 4  

x=4

The solution is x=4

Part 3)

we have

x\geq 0 -----> inequality A

The solution of the inequality A is in the first and fourth quadrant

y\geq 0 -----> inequality B

The solution of the inequality B is in the first and second quadrant

so

the solution of the inequality A and the inequality B is the first quadrant

Part 4) Which ordered pair is a solution of the inequality?

we have

y\geq 4x-5

we know that

If a ordered pair is a solution  of the inequality

then

the ordered pair must be satisfy the inequality

we're going to verify all the cases

<u>case A)</u> point (3,4)

Substitute the value of x and y in the inequality

x=3,y=4

4\geq 4(3)-5

4\geq 7 ------> is not true

therefore

the point (3,4) is not a solution of the inequality

<u>case B)</u> point (2,1)

Substitute the value of x and y in the inequality

x=2,y=1

1\geq 4(2)-5

1\geq 3 ------> is not true

therefore

the point  (2,1) is not a solution of the inequality

<u>case C)</u> point (3,0)

Substitute the value of x and y in the inequality

x=3,y=0

0\geq 4(3)-5

0\geq 7 ------> is not true

therefore

the point  (3,0) is not a solution of the inequality

<u>case D)</u> point (1,1)

Substitute the value of x and y in the inequality

x=1,y=1

1\geq 4(1)-5

1\geq -1 ------> is true

therefore

the point  (1,1) is  a solution of the inequality

Part 5) Write an inequality to match the graph

we know that

The equation of the line has a negative slope

The y-intercept is the point (3,0)

The x-intercept is a positive number

The solution is the shaded area above the dashed line

so

the equation of the line is y=-5x+3

The inequality is  y>-5x+3

3 0
3 years ago
Read 2 more answers
A chef uses 4 3/4 cups of broth for 10 servings of soup. How much broth is used in one serving of soup?
sukhopar [10]

Answer:

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Step-by-step explanation:

3 0
3 years ago
A school baseball team raised $810 for new uniforms.Each player sold 1 book of tickets.There were 10 tickets in a book and each
Leviafan [203]

Answer:

The school baseball team sold 270 tickets

Step-by-step explanation:

Step 1

Identify the total amount of tickets sold by each player;

1 player=1 book of tickets

But 1 book=10 tickets

Step 2

Express the total cost of ticket sales per book as follows;

total cost=cost per ticket×number of tickets per book

where;

cost per ticket=$3

number of tickets per book=10

replacing;

total cost=(3×10)=$30

Step 3

Using the expression below, solve for the number of tickets sold

Total amount raised=price per ticket×number of tickets sold

where;

total amount raised=$810

price per ticket=$3

number of tickets sold=n

replacing;

810=3×n

3 n=810

n=810/3=270

n=270

The school baseball team sold 270 tickets

5 0
3 years ago
the length of a rectangle is 5 inches longer than twice the width and the area is 12 inches squared. Let l represent the length
svet-max [94.6K]

Answer:

Length = 8 inch , Width = \frac{3}{2} , This equation models the situation

Step-by-step explanation:

Given as ;

The Area of Rectangle is 12 inches²

The Length of Rectangle is 5 inches longer than twice the width

Let The Length = L inches

      The Width   = W inches

According to question ,

L = 5 + (2 × w )

∵ The Area of Rectangle = Length × width

Or, 12  inches²  = [ 5 + (2 × w ) ] ×  w

Or,  12  inches² = 5 w +2 w²

Or,  2 w² + 5 w  - 12 = 0

Or,   2 w² + 8 w  -3 w - 12 = 0

Or,  2 w (w +4) - 3 (w + 4) = 0

I.e (w + 4) ( 2 w - 3) = 0

So ,  w = -4 , and w = \frac{3}{2}

∴  Length = 5 + (2 × w ) =

   Length = 5 + (2 ×\frac{3}{2}  )  

so ,  L = 5 + 3 = 8

Hence Length = 8 inch , Width = \frac{3}{2}   This equation models the situation Answer

3 0
3 years ago
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