Question

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.

Answer 1

Answer:

see the explanation

Step-by-step explanation:

we have

$f(x)=\sqrt{-x}$

we know that

The radicand of the function cannot be a negative number

so

$-x\geq 0$

Solve for x

Multiply by -1 both sides

$x\leq 0$

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

$144\leq 0$ ----> is not true

This value of x not satisfy the domain

substitute

$f(x)=\sqrt{-144}$ ----> this value is undefined

For x=-144

$-144\leq 0$ ----> is true

This value of x satisfy the domain

substitute

$f(x)=\sqrt{-(-144)}$

$f(x)=\sqrt{144}$----> 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

Answer 2

Answer:

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.