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.

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Step-by-step explanation:

we have

we know that

The radicand of the function cannot be a negative number

so

Solve for x

Multiply by -1 both sides

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

----> is not true

This value of x not satisfy the domain

substitute

----> this value is undefined

For x=-144

----> is true

This value of x satisfy the domain

substitute

----> 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

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