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.
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.
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.
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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.