QuestionDetermine the domain of the function $f(x) = \frac{x}{\sqrt{x-8}}$ .

Studdy Solution

STEP 1

Assumptions1. The function is given as $\frac{x}{\sqrt{x-8}}$ . The domain of a function is the set of all possible input values (x-values) which will produce a valid output.
3. For this function, the denominator cannot be zero and the value under the square root must be greater than or equal to zero (since we cannot take the square root of a negative number).

STEP 2

First, we need to find the values of x for which the denominator is not zero. This is because division by zero is undefined in mathematics. So we set the denominator equal to zero and solve for x.
$\sqrt{x-8} =0$

STEP 3

To solve for x, we need to square both sides of the equation to get rid of the square root.
$(\sqrt{x-8})^2 =0^2$

STEP 4

This simplifies to $x-8 =0$

STEP 5

olving for x gives $x =8$ So, x cannot be8 because it would make the denominator zero.

STEP 6

Next, we need to find the values of x for which the value under the square root is greater than or equal to zero. This is because the square root of a negative number is not a real number. So we set the value under the square root greater than or equal to zero and solve for x.
$x-8 \geq0$

STEP 7

olving for x gives $x \geq$

STEP 8

Combining the results from steps5 and7, we find that the domain of the function is all x such that x is greater than8. However, x cannot be equal to8 because it would make the denominator zero.
So, the domain of the function is $x >8$

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QuestionDetermine the domain of the function $f(x) = \frac{x}{\sqrt{x-8}}$ .

Studdy Solution

STEP 1

STEP 2

First, we need to find the values of x for which the denominator is not zero. This is because division by zero is undefined in mathematics. So we set the denominator equal to zero and solve for x.
$\sqrt{x-8} =0$

STEP 3

To solve for x, we need to square both sides of the equation to get rid of the square root.
$(\sqrt{x-8})^2 =0^2$

STEP 4

This simplifies to $x-8 =0$

STEP 5

olving for x gives $x =8$ So, x cannot be8 because it would make the denominator zero.

STEP 6

Next, we need to find the values of x for which the value under the square root is greater than or equal to zero. This is because the square root of a negative number is not a real number. So we set the value under the square root greater than or equal to zero and solve for x.
$x-8 \geq0$

STEP 7

olving for x gives $x \geq$

STEP 8

Combining the results from steps5 and7, we find that the domain of the function is all x such that x is greater than8. However, x cannot be equal to8 because it would make the denominator zero.
So, the domain of the function is $x >8$

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QuestionDetermine the domain of the function f(x)=xx−8f(x) = \frac{x}{\sqrt{x-8}}f(x)=x−8​x​.

Studdy Solution

STEP 1

STEP 2

First, we need to find the values of x for which the denominator is not zero. This is because division by zero is undefined in mathematics. So we set the denominator equal to zero and solve for x.x−8=0\sqrt{x-8} =0x−8​=0

STEP 3

To solve for x, we need to square both sides of the equation to get rid of the square root.(x−8)2=02(\sqrt{x-8})^2 =0^2(x−8​)2=02

STEP 4

This simplifies tox−8=0x-8 =0x−8=0

STEP 5

olving for x givesx=8x =8x=8So, x cannot be8 because it would make the denominator zero.

STEP 6

STEP 7

olving for x givesx≥x \geqx≥

STEP 8

Combining the results from steps5 and7, we find that the domain of the function is all x such that x is greater than8. However, x cannot be equal to8 because it would make the denominator zero.So, the domain of the function isx>8x >8x>8

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QuestionDetermine the domain of the function $f(x) = \frac{x}{\sqrt{x-8}}$ .

First, we need to find the values of x for which the denominator is not zero. This is because division by zero is undefined in mathematics. So we set the denominator equal to zero and solve for x.
$\sqrt{x-8} =0$

To solve for x, we need to square both sides of the equation to get rid of the square root.
$(\sqrt{x-8})^2 =0^2$

This simplifies to $x-8 =0$

olving for x gives $x =8$ So, x cannot be8 because it would make the denominator zero.

olving for x gives $x \geq$

Combining the results from steps5 and7, we find that the domain of the function is all x such that x is greater than8. However, x cannot be equal to8 because it would make the denominator zero.
So, the domain of the function is $x >8$