Question

Which function is undefined for x = 0?

Answer 1

Answer:

$y=\sqrt{x-2}$

Step-by-step explanation:

we know that

The domain of a function is the set of all possible values of x

Verify each case

case 1) we have

$y=\sqrt[3]{x-2}$

The domain is the interval (-∞,∞)

therefore

The function is defined for all real numbers

case 2) we have

$y=\sqrt{x-2}$

Remember that the radicand must be greater than or equal to zero

so

$x-2\geq 0$

solve for x

$x\geq 2$

The domain is the interval [2,∞)

therefore

The function is undefined for x=0

case 3) we have

$y=\sqrt[3]{x+2}$

The domain is the interval (-∞,∞)

therefore

The function is defined for all real numbers

case 4) we have

$y=\sqrt{x+2}$

Remember that the radicand must be greater than or equal to zero

so

$x+2\geq 0$

solve for x

$x\geq-2$

The domain is the interval [-2,∞)

The number zero is included in the domain

therefore

The function is defined for all real numbers greater than or equal to -2 (function is defined for x=0)

Answer 2

Answer:

D

Step-by-step explanation: