QuestionFind the domain of $f(x)=\sqrt{6x-48}$ . Answer in interval notation: $\square$ .

Studdy Solution

STEP 1

Assumptions1. The function is $f(x)=\sqrt{6x-48}$ . . We need to find the domain of this function.
3. The domain of a function is the set of all possible input values (x-values) which will produce a valid output.
4. For a square root function, the expression inside the square root must be greater than or equal to zero, because the square root of a negative number is not a real number.

STEP 2

To find the domain of the function, we need to set the expression inside the square root greater than or equal to zero.
$6x-48 \geq0$

STEP 3

Now, solve the inequality for x.
First, add48 to both sides of the inequality to isolate the term with x on one side.
$6x \geq48$

STEP 4

Next, divide both sides of the inequality by6 to solve for x.
$x \geq \frac{48}{6}$

STEP 5

Calculate the value of x.
$x \geq8$ So, the domain of the function $f(x)=\sqrt{x-48}$ is $x \geq8$ .

STEP 6

Express the domain in interval notation. In interval notation, the domain is written as an interval from the smallest x value to the largest x value.For $x \geq8$ , the interval is $[8, \infty)$ .
So, the domain of the function $f(x)=\sqrt{6x-48}$ is $[8, \infty)$ .

Was this helpful?

QuestionFind the domain of $f(x)=\sqrt{6x-48}$ . Answer in interval notation: $\square$ .

Studdy Solution

STEP 1

STEP 2

To find the domain of the function, we need to set the expression inside the square root greater than or equal to zero.
$6x-48 \geq0$

STEP 3

Now, solve the inequality for x.
First, add48 to both sides of the inequality to isolate the term with x on one side.
$6x \geq48$

STEP 4

Next, divide both sides of the inequality by6 to solve for x.
$x \geq \frac{48}{6}$

STEP 5

Calculate the value of x.
$x \geq8$ So, the domain of the function $f(x)=\sqrt{x-48}$ is $x \geq8$ .

STEP 6

Express the domain in interval notation. In interval notation, the domain is written as an interval from the smallest x value to the largest x value.For $x \geq8$ , the interval is $[8, \infty)$ .
So, the domain of the function $f(x)=\sqrt{6x-48}$ is $[8, \infty)$ .

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionFind the domain of f(x)=6x−48f(x)=\sqrt{6x-48}f(x)=6x−48​. Answer in interval notation: □\square□.

Studdy Solution

STEP 1

STEP 2

To find the domain of the function, we need to set the expression inside the square root greater than or equal to zero.6x−48≥06x-48 \geq06x−48≥0

STEP 3

Now, solve the inequality for x.First, add48 to both sides of the inequality to isolate the term with x on one side.6x≥486x \geq486x≥48

STEP 4

Next, divide both sides of the inequality by6 to solve for x.x≥486x \geq \frac{48}{6}x≥648​

STEP 5

Calculate the value of x.x≥8x \geq8x≥8So, the domain of the function f(x)=x−48f(x)=\sqrt{x-48}f(x)=x−48​ is x≥8x \geq8x≥8.

STEP 6

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionFind the domain of $f(x)=\sqrt{6x-48}$ . Answer in interval notation: $\square$ .

To find the domain of the function, we need to set the expression inside the square root greater than or equal to zero.
$6x-48 \geq0$

Now, solve the inequality for x.
First, add48 to both sides of the inequality to isolate the term with x on one side.
$6x \geq48$

Next, divide both sides of the inequality by6 to solve for x.
$x \geq \frac{48}{6}$

Calculate the value of x.
$x \geq8$ So, the domain of the function $f(x)=\sqrt{x-48}$ is $x \geq8$ .