Mathematics : asked on loriswaim

25.07.2021

What is the graph of this function? F(x)=||x||+2/2 If 0<x<6

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19.08.2022, solved by verified expert

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Note - There is an error in the interval of the function. For step function, the interval of the function should be either 0≤x<6 or 0<x≤6. I will calculate for both the interval.

Given function is,

F(x) = (|x|+2)/2 for 0≤x<6

Putting x = 0, F(x) = 1

Putting x = 1, F(x) = 1.5

Putting x = 2, F(x) = 2

Putting x = 3, F(x) = 2 5

Putting x = 4, F(x) = 3

Putting x = 5, F(x) = 3.5

Thus, option C would be correct.

Given function is,

F(x) = (|x|+2)/2 for 0<x≤6

Putting x = 1, F(x) = 1.5

Putting x = 2, F(x) = 2

Putting x = 3, F(x) = 2 5

Putting x = 4, F(x) = 3

Putting x = 5, F(x) = 3.5

Putting x = 6, F(x) = 4

Thus, option E would be correct.

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Mathematics

Look at the function f(x)=x^2-2. which of the following describes the domain and range of the function and its inverse?

Step-by-step answer

P Answered by Master

9

A

Step-by-step explanation:

The function is a quadratic whose graph is a parabola. All parabolas have no limitations on their domain. This means the domain of the function is all real numbers.

This parabola has a minimum value since its leading coefficient is positive. Its vertex is at (0,-2). This means its range is all values greater than -2 or y ≥ -2.

An inverse of a function is its reflection across the y=x line. This results in (x,y) in the function becoming (y,x) in its inverse. The domain of the function becomes the range of the inverse and the range of the function becomes the domain of the inverse. Inverse has x ≥ -2 as its domain and all real numbers for its range.

Mathematics

Look at the function f(x)=x^2-2. which of the following describes the domain and range of the function and its inverse?

Step-by-step answer

P Answered by Master

9

A

Step-by-step explanation:

The function is a quadratic whose graph is a parabola. All parabolas have no limitations on their domain. This means the domain of the function is all real numbers.

This parabola has a minimum value since its leading coefficient is positive. Its vertex is at (0,-2). This means its range is all values greater than -2 or y ≥ -2.

An inverse of a function is its reflection across the y=x line. This results in (x,y) in the function becoming (y,x) in its inverse. The domain of the function becomes the range of the inverse and the range of the function becomes the domain of the inverse. Inverse has x ≥ -2 as its domain and all real numbers for its range.

Mathematics

What is the value of the range of the function f(x)=x^2+2 for the domain value 1/4? a. y = 2 b. y = 2 1/4 c. y = 2 1/8 d. y = 2 1/16

Step-by-step answer

P Answered by PhD

72

F(x) = x^2 + 2
f(1/4) = (1/4)^2 + 2 = 1/16 + 2 = 2 1/16

Mathematics

What is the value of the range of the function f(x)=x^2+2 for the domain value 1/4? a. y = 2 b. y = 2 1/4 c. y = 2 1/8 d. y = 2 1/16

Step-by-step answer

P Answered by PhD

72

F(x) = x^2 + 2
f(1/4) = (1/4)^2 + 2 = 1/16 + 2 = 2 1/16

Mathematics

Acellus Complete the data table for the function f(x) = -x-2 + 2. Х -2 -3 -6 -11 Y [?] Enter

Step-by-step answer

P Answered by Master

x= -6 —> y= 4

x= -11 —> y= 5

Step-by-step explanation:

x= -6 —> y= 4

$f( - 6) = \sqrt{ - ( - 6) - 2} + 2 \\ = \sqrt{6 - 2} + 2 \\ = \sqrt{4} + 2 \\ = 2 + 2 \\ = 4$

x= -11 —> y= 5

$f( - 11) = \sqrt{ - ( - 11) - 2} + 2 \\ = \sqrt{11 - 2} + 2 \\ = \sqrt{9} + 2 \\ = 3 + 2 \\ = 5$

I hope I helped you^_^

Mathematics

Acellus Complete the data table for the function f(x) = -x-2 + 2. Х -2 -3 -6 -11 Y [?] Enter

Step-by-step answer

P Answered by Specialist

x= -6 —> y= 4

x= -11 —> y= 5

Step-by-step explanation:

x= -6 —> y= 4

$f( - 6) = \sqrt{ - ( - 6) - 2} + 2 \\ = \sqrt{6 - 2} + 2 \\ = \sqrt{4} + 2 \\ = 2 + 2 \\ = 4$

x= -11 —> y= 5

$f( - 11) = \sqrt{ - ( - 11) - 2} + 2 \\ = \sqrt{11 - 2} + 2 \\ = \sqrt{9} + 2 \\ = 3 + 2 \\ = 5$

I hope I helped you^_^

Mathematics

Determine the range of the function f(x)=x^2-2/2 when the domain is {0, 2}.

Step-by-step answer

P Answered by PhD

The range of function is { -1, 1 }

Solution:

Given that, the function is:

$f(x) = \frac{x^2-2}{2}$

Domain is {0, 2 }

We have to find the range of function

The domain refers to the set of possible input values

The range is the set of possible output values

Here domain is x = 0 and x = 2

Substitute x = 0 in given function

$f(0) = \frac{0-2}{2}\\\\f(0) = \frac{-2}{2}\\\\f(0) = -1$

Substitute x = 2 in given function

$f(2) = \frac{2^2-2}{2}\\\\f(2) = \frac{4-2}{2}\\\\f(2) = \frac{2}{2} = 1$

Thus the range of function is { -1, 1 }

Mathematics

Consider the function f(x) = x^2 +2 sqrt{x}. Evaluate 2f(2) - f(8).

Step-by-step answer

P Answered by PhD

-56 + 3 sqrt(2) /2

Step-by-step explanation:

f(x) = x^2 +2/sqrt{x}.

2f(2) - f(8).

First find f(2)

f(2) = 2^2 +2/sqrt{2} = 4 + 2/ sqrt(2)

Then f(8)

f(8) = 8^2 +2/sqrt{8} = 64 + 2 / sqrt(4)sqrt(2) = 64+ 2/2sqrt(2) = 64 + 1/ sqrt(2)

2f(2) - f(8).

2 * (4 + 2/ sqrt(2)) - (64 + 1/ sqrt(2))

8 + 4/ sqrt(2) - 64 - 1/ sqrt(2)

Combine like terms

-56 + 3 / sqrt(2)

Rationalizing the second term

-56 + 3/ sqrt(2) * sqrt(2)/sqrt(2)

-56 + 3 sqrt(2) /2

Mathematics

What is the range of the function f(x) = x^2 + 2 when the domain is (-1, 0, 1)?

Step-by-step answer

P Answered by PhD

The range: {2, 3}

Step-by-step explanation:

We have the function:

f(x)=x^2+2

The domain:

$x\in\{-1,\ 0,\ 1\}$

The range:

put the values of , and calculate the value of f(x):

for x = -1:

f(-1)=(-1)^2+2=1+2=3

for x = 0:

f(0)=0^2+2=0+2=2

for x = 1:

f(1)=1^2+2=1+2=3

$y\in\{2,\ 3\}$

Mathematics

What is the value of the range of the function f(x)=x^2+2 for the domain value 1/4?

Step-by-step answer

P Answered by PhD

11

Subst. 1/4 for x in f(x) = x^2 + 2: f(1/4) = (1/4)^2 + 2 = 1/16 + 2 = 2 1/16

This is the range when the domain is 1/4. Usually a domain contains more than one number.

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