QuestionIdentify values to exclude from the domain of $\frac{x^{2}}{x^{2}+16}$ . Options: $x=5$ , $x=4$ , $x=0$ , $x=-4$ . Select all that apply.

Studdy Solution

STEP 1

Assumptions1. The expression is $\frac{x^{}}{x^{}+16}$ . . We need to find the values of $x$ that must be excluded from the domain.
3. The domain of a function or expression is the set of all possible input values (in this case, $x$ values) that will output real numbers.

STEP 2

The denominator of a fraction cannot be zero because division by zero is undefined in mathematics. Therefore, we need to find the values of $x$ that make the denominator zero.
The denominator of our expression is $x^{2}+16$ .

STEP 3

Set the denominator equal to zero and solve for $x$ .
$x^{2}+16=0$

STEP 4

Subtract16 from both sides of the equation to isolate $x^{2}$ .
$x^{2}=-16$

STEP 5

Take the square root of both sides of the equation to solve for $x$ . Remember that the square root of a number is both its positive and negative root.
$x=\pm\sqrt{-16}$

STEP 6

The square root of a negative number is not a real number, so there are no real values of $x$ that make the denominator zero.
Therefore, there are no values that need to be excluded from the domain of the given expression.
Checking the provided options $x=5$ , $x=4$ , $x=0$ , and $x=-4$ are all valid values for the domain of the expression.So, the correct answer is "None".

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QuestionIdentify values to exclude from the domain of $\frac{x^{2}}{x^{2}+16}$ . Options: $x=5$ , $x=4$ , $x=0$ , $x=-4$ . Select all that apply.

Studdy Solution

STEP 1

Assumptions1. The expression is $\frac{x^{}}{x^{}+16}$ . . We need to find the values of $x$ that must be excluded from the domain.
3. The domain of a function or expression is the set of all possible input values (in this case, $x$ values) that will output real numbers.

STEP 2

The denominator of a fraction cannot be zero because division by zero is undefined in mathematics. Therefore, we need to find the values of $x$ that make the denominator zero.
The denominator of our expression is $x^{2}+16$ .

STEP 3

Set the denominator equal to zero and solve for $x$ .
$x^{2}+16=0$

STEP 4

Subtract16 from both sides of the equation to isolate $x^{2}$ .
$x^{2}=-16$

STEP 5

Take the square root of both sides of the equation to solve for $x$ . Remember that the square root of a number is both its positive and negative root.
$x=\pm\sqrt{-16}$

STEP 6

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QuestionIdentify values to exclude from the domain of x2x2+16\frac{x^{2}}{x^{2}+16}x2+16x2​. Options: x=5x=5x=5, x=4x=4x=4, x=0x=0x=0, x=−4x=-4x=−4. Select all that apply.

Studdy Solution

STEP 1

Assumptions1. The expression is xx+16\frac{x^{}}{x^{}+16}x+16x​. . We need to find the values of xxx that must be excluded from the domain.3. The domain of a function or expression is the set of all possible input values (in this case, xxx values) that will output real numbers.

STEP 2

The denominator of a fraction cannot be zero because division by zero is undefined in mathematics. Therefore, we need to find the values of xxx that make the denominator zero.The denominator of our expression is x2+16x^{2}+16x2+16.

STEP 3

Set the denominator equal to zero and solve for xxx.x2+16=0x^{2}+16=0x2+16=0

STEP 4

Subtract16 from both sides of the equation to isolate x2x^{2}x2.x2=−16x^{2}=-16x2=−16

STEP 5

Take the square root of both sides of the equation to solve for xxx. Remember that the square root of a number is both its positive and negative root.x=±−16x=\pm\sqrt{-16}x=±−16​

STEP 6

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QuestionIdentify values to exclude from the domain of $\frac{x^{2}}{x^{2}+16}$ . Options: $x=5$ , $x=4$ , $x=0$ , $x=-4$ . Select all that apply.

Assumptions1. The expression is $\frac{x^{}}{x^{}+16}$ . . We need to find the values of $x$ that must be excluded from the domain.
3. The domain of a function or expression is the set of all possible input values (in this case, $x$ values) that will output real numbers.

The denominator of a fraction cannot be zero because division by zero is undefined in mathematics. Therefore, we need to find the values of $x$ that make the denominator zero.
The denominator of our expression is $x^{2}+16$ .

Set the denominator equal to zero and solve for $x$ .
$x^{2}+16=0$

Subtract16 from both sides of the equation to isolate $x^{2}$ .
$x^{2}=-16$

Take the square root of both sides of the equation to solve for $x$ . Remember that the square root of a number is both its positive and negative root.
$x=\pm\sqrt{-16}$