For each function, find the inverse and the domain and range of the function and its inverse. Determine whether the inverse is a function. f(x)=x²/2

The domain of the function is: [-1, 10]

And the range of the function is: [-1,0,1,2,3,4,5,6,7,8,,9,10]

According to the question, the intervals can be defined by a common difference of one value.

Therefore, the domain of the function is: [-1, 10]

And the range of the function is: [-1,0,1,2,3,4,5,6,7,8,,9,10]

What is domain and range in the function?

The domain of a function can be defined as the complete set of all the possible values for the dependent variables. Similarly, the range of the function can be expressed as the set of all the values which can be assumed by the expression of the function.

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Answer:

the equation is " y = (slope)x + (y-intercept) "

Step-by-step explanation:

here ya go ! hope this helps

Answer: Hope this helps. This graph is at a highschool level so if you are actually in highschool this should help you. If you are in middle school I can adjust it to a more simple graph.

Step-by-step explanation:

No extraneous solution to the equation.

The equation is:

3[tex]\sqrt{2x}[/tex] - 3= 9

To know whether the equation has an extraneous solution, first we need to find the value of x.

[tex]3\sqrt{2x}[/tex] = 12

[tex]\sqrt{2x}[/tex] = 4

2x = 16

x = 8

Now put the value of x in the equation.

3[tex]\sqrt{2 * 8}[/tex] - 3 = 9

3× 4 - 3 = 9

12 - 3= 9

9 = 9

Therefore there is no extraneous solution to the equation, x = 8 is the solution of the equation.

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Answer: 59 eggs

Step-by-step explanation: Dividing 3 will get you 19 eggs with 2 left over.  Dividing 59 by 5 will get you 11 eggs and 4 left over

Answer:

II and III

Step-by-step explanation:

I.

-9 - 5x > -1

-9 - 5(2) > -1

-9 - 10 > -1

-19 > -1

False

II.

-9 - 5x > -1

-9 - 5(-5) > -1

-9 + 25 > -1

16 > -1

True

III.

-9 - 5(-10) > -1

-9 + 50 > -1

41 > -1

true

I hope this helps!

Answer:

Step-by-step explanation:

Also written as-

 4x - 27 = x

     + 27  +27

(add 27 to both sides)

The new equation would be written as-

 4x = x + 27

  -x   -x

(subtract x from both sides)

  [tex]3x = 27 \\ \\ \frac{3x}{3} =\frac{27}{3} \\ \\ x=9[/tex]

The number is 9

Answer:

[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

[tex]\frac{d}{dx}\left(\frac{x}{2}-\frac{1}{3}\right)[/tex]

= [tex]\frac{d}{dx}\left(\frac{x}{2}\right)-\frac{d}{dx}\left(\frac{1}{3}\right)[/tex]

=[tex]\frac{1}{2}\frac{d}{dx}\left(x\right) - 0[/tex]

= [tex]\frac{1}{2} - 0[/tex]

= [tex]\frac{1}{2}[/tex]

Hope this helps! :) please leave a rating and brainliest if this was useful!

Answer:

10.083333...ft

Step-by-step explanation:

length = 12ft

area = 121sqft

area = length * width

121sqft = 12ft * width

width = 121sqft / 12ft

[tex]width = 10\frac{1}{12}\mathrm{ft}[/tex]

width = 10.08(3)ft

Answer:

angles 1 and 5

Step-by-step explanation:

The two angles are said to be adjacent angles when they share the common vertex and side.

so angles 1 and 5 are adjacent angles

The polynomial function is [tex]x^{2}-x-2ix+\sqrt{7}x-\sqrt{7}-2\sqrt{7}i[/tex]

In mathematics, polynomial function can be defined as the equation which consist of coefficient, variables and exponents. A polynomial equation has positive numbers as their exponent which is also known as its degree. All the equations such as quadratic equation, cubic equation which has non  negative number as their powers are part of polynomial equation.

Types of polynomial equations :

Some examples of polynomial equation are :

According to question,

roots are -√7 , 1+2i

Thus the factors are :

(x - (-√7)) (x-(1+2i))

=> (x+√7)(x-1-2i)

=>x²-x-2ix+√7x-√7-√7.2i

Thus polynomial function for given roots is x²-x-2ix+√7x-√7-√7.2i.

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The rational number between the square root of 7 and the square root of 8 is 27/10

Rational expressions are expressions that are represented by the quotient of two polynomials or radicals.

This means that, a rational expression is represented by a fraction whose numerator and denominator are polynomials or radicals

The features of the rational number are given as

Value = between the square root of 7 and the square root of 8

Rewrite the value properly

So, we have

Value = between √7 and √8

Evaluate the values of √7 and √8

So, we have

√7 = 2.65

√8 = 2.83

This means that the rational number is between 2.65 and 2.83

A number between 2.65 and 2.83 is 2.7

Express as fraction

value = 27/10

Hence, the rational number between the square root of 7 and the square root of 8 is 27/10

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Answer: the answer is no solution

Step-by-step explanation:

Answer:

No Solution

Step-by-step explanation:

An absolute value will always have a positive value. If you isolate the absolute value it shows the abs val LESS THAN a negative number. Its not possible to have a positive less than a negative.

If you just go on and do the problem in auto-pilot, the answers don't check. ALSO since it it a LESS THAN inequality statement BOTH of the inequalities have to be true at the same time which is not possible.

See image.

Answer:

23/30

Step-by-step explanation:

4/15= 8/30

1/2= 15/30

8/30+15/30= 23/30

Answer:

True

it represents 2/3 because it has 1/1 in each question

Answer: 224 calories ==> 1st option

Step-by-step explanation:

1 serving * 1,120 calories/ 5 servings=

1*1120/5=

1*224=224 calories ==> 1st option

Answer:

Step-by-step explanation:

224 calories I think

Answer:

Brainliest pls

Step-by-step explanation:

-20

Answer:

The answer is -20.

Step-by-step explanation:

REMEMBER THIS:

Please excuse my dear aunt sally…

PLEASE = PARENTHESIS

EXCUSE= EQUATION

MY = MULTIPLICATION

DEAR = DIVISION

AUNT = ADDITION

SALLY = SUBTRACTION

^In that order^

Remember to use this statement to remember how to simplify the expression. PEMDAS.

Answer:

B

Step-by-step explanation:

6x - 8x - 4 = - 2x - 2 , that is

- 2x - 4 = - 2x - 2 ( add 4 to both sides )

- 2x = - 2x + 2 ( add 2x to both sides )

0 = 2 ← not possible

this indicates the equation has no solution

Answer:

6x-8x-4=-2x-2 (group the like terms)

6x-8x+2x= 4-2 (-8x+2x= -6x and 6x-6x=0) (4-2=2)

answer= 0=2

,therefore: it has no solution

Step-by-step explanation:

the answer is 0=2 which mean there is nothing that 2 is equivalent to because when you group the like terms and work out the answer the x in the equation will be canceled.

After solving the equation ln 3x =6, the value of x is equal to [tex]\frac{e^6}{3}[/tex]

We have been asked to find x in ln 3 x=6

⇒ ln 3 x = 6

⇒ 3x = [tex]e^6[/tex]

⇒ x = [tex]\frac{e^6}{3}[/tex]

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

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The cost of the Ginnie's dinner is a $40 and the cost of his cousin's dinner is $25.

According to the statement

We have to find that the cost of their dinners.

So, For this purpose, we all know that the

The cost function may be wont to find the common cost, which is that the average amount of cash it costs to provide a unit.

From the given information:

Ginnie dinner cost $15 over her cousin's. If their combined bill was under $65.

Then

Let Ginnie dinner is x and his cousin's be y.

Then

x+y = 65 And x = y+15

Then

Substitute the values then y+15+y = 652

y+15 = 652

y = 65-152

y = 50

[tex]y = \frac{50}{2}[/tex]

y = 25.

Then x = y+15

x = 25+15

x = 40.

So, The cost of the Ginnie's dinner is a $40 and the cost of his cousin's dinner is $25.

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-7 = extraneous solution

The equation is

[tex]\sqrt{-3x - 5}[/tex] = x + 3

To find the value of x we need to square both sides of the equation

[tex](\sqrt{-3x - 5})^{2}[/tex] = [tex](x + 3)^{2}[/tex]

- 3x -5 = [tex]x^{2}[/tex] + 6x + 9

[tex]x^{2}[/tex] + 9x + 14 = 0

[tex]x^{2}[/tex] + 7x + 2x + 14 =0

x( x + 7) + 2( x + 7) = 0

(x + 7) (x + 2 ) = 0

x = -2, -7

To find the extraneous solution we have to put both the value of x in the equation.

x=-2

[tex]\sqrt{(-3 * -2) - 5}[/tex] = -2 +3

[tex]\sqrt{1}[/tex] = 1

1 = 1

x = -7

[tex]\sqrt{(-3 * -7) - 5}[/tex] = -7 +3

[tex]\sqrt{16}[/tex] = -4

4 = -4

The extraneous solution of the equation is -7 and -2 is the solution of the equation

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Answer:

0,3 I think

Step-by-step explanation:

if you ever need help with questions like these, m a t h w a y works for me

Answer:

Step-by-step explanation:oooooooooooooooooooooooooooooooooooooo

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The divide and simplify of the equation √36 x⁴ / √9 x⁶ will result to  [tex]\frac{2}{x^{2} }[/tex]

Let's begin by simplifying the equation;

Simplify the equation by finding the square root of both 36 and 9

The square root of 36= 6

The square root of 9= 3

= [tex]\frac{6x^{4} }{3x^{6} }[/tex]

The above equation can also be written as;

=  [tex]6x^{4} * 3x^{-6}[/tex]

The next step is to solve the powers, that is,

=   [tex]\frac{6x^{4} }{3x^{6} }[/tex]

Cancel out 6 by 3 and get  2

The result is,  

=  [tex]\frac{2}{x^{6-4} }[/tex]

The final submission result is,

=  [tex]\frac{2}{x^{2} }[/tex]

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Using a proportional relationship, it is found that point (10.5, 42) makes sense in this context, as when x = 10.5, y = 42 is the output of the relation.

A proportional relationship is a function in which the output variable is given by the multiplication of the input variable and the constant of proportionality, defined by k, in the case of a direct relationship, according to the following rule:

y = kx

For the case of an inverse relationship, we have that:

y = k/x.

From the table in this problem, the constant is given as follows:

k = 28/7 = 32/8 = 36/9 = 40/10 = 4.

Hence the relation is modeled as follows:

y = 4x.

In which:

When x = 10.5, we have that:

y = 4(10.5) = 42.

Hence point (10.5, 42) makes sense in this context.

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Answer:

m is always the number in front of x

y=mx+c

so m=-3

Step-by-step explanation:

Answer:V = LWH volume = length x width x height240 = (2+H)((6+H)H  = (H^2 + 8H + 12)H =  H^3 + 8H^2 + 12HH^3 + 8H^2 + 12H - 240 = 0while there's no easy way to solve cubics,  try some simple integers.  You need an even integer2 doesn't work,  too small, try 44^3 + 8(4)^2 + 12(4) -240 =0   Height = 4 feetdimensions are 4 x 10 x 6  feet   = 240 ft/63divide h-4 into the cubic to get H^2 + 12H + 60the discriminate = 144-4(60) < 0 so there are no other real solutions4 feet by 6 feet by 10 feet is the only solution

Step-by-step explanation:

Answer:

D Maxwell drove further. He drove 18 miles.

Step-by-step explanation:

Distance = Speed × Time

Maxwell:

Distance = 45 × 0.4

Distance = 18 miles

Bianca:

Distance = 65 ×0.25

Distance = 16.25 miles

18 > 16.25

Maxwell drove further. He drove 18 miles.

Answer:

D. Maxwell. He drove 18 miles,

Step-by-step explanation:

Distance = speed * time

Maxwell drives:

45 * 0.4 = 18 miles.

Bianca drove:

65 * 0.25 = 16.25 miles.