F(x)= StartRoot negative x EndRoot?

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F(x)= StartRoot negative x EndRoot?

F(x)= StartRoot negative x EndRoot?

is c in the future if you want to talk about it and let me know if you need anything else

explanation

Step-by-step explanation:

The square root of a negative number, such as StartRoot negative 144 EndRoot, is undefined. Explain why the square root of –x, StartRoot negative x EndRoot, is not necessarily undefined and what this means about the domain and range of f(x) = StartRoot negative x EndRoot.

see the explanation

Step-by-step explanation:

we have

[tex]f(x)=\sqrt{-x}[/tex]

we know that

The radicand of the function cannot be a negative number

so

[tex]-x\geq 0[/tex]

Solve for x

Multiply by -1 both sides

[tex]x\leq 0[/tex]

The domain of the function f(x) is the interval -----> (-∞, 0]

The domain is all real numbers less than or equal to zero

The range of the function f(x) is the interval ----> [0,∞)

The range is all real numbers greater than or equal to zero

Example

For x=144

[tex]144\leq 0[/tex] ----> is not true

This value of x not satisfy the domain

substitute

[tex]f(x)=\sqrt{-144}[/tex] ----> this value is undefined

For x=-144

[tex]-144\leq 0[/tex] ----> is true

This value of x satisfy the domain

substitute

[tex]f(x)=\sqrt{-(-144)}[/tex]

[tex]f(x)=\sqrt{144}[/tex]----> this value is defined

therefore

The function will be undefined for all those values of x that do not belong to the interval of the domain of the function

f(x) = √-x

Step-by-step explanation:

f(x) = √-x

Step 1: Obtain the value of x (start)

Step 2: The square root of -x

Step 3: Write down the value of f(x) (End)

It has the same domain as the function [tex]f(x)=-\sqrt{-x}[/tex].

Step-by-step explanation:

The function ...

[tex]f(x)=\sqrt{-x}[/tex]

has a domain of all non-positive numbers and a range of all non-negative numbers. Anything with a -x under the radical will have the same domain. Any positive root will have the same range.

__

So, we can say it has the same domain as ...

[tex]f(x)=-\sqrt{-x}[/tex]

If x is a negative number, then negative x is a positive number and the square root can be determined. Therefore, the domain of the function is x ≤ 0. As a result, the range is never negative either, so it is y ≥0.