Math / Algebra

QuestionFind the domain of the function. $g(x)=\sqrt{16+2 x}$
Write your answer using interval notation. \begin{tabular}{|c|} \hline \multirow[t]{3}{*}{(1.ㄴ]} \\ \hline \\ \hline \\ \hline \end{tabular}

Studdy Solution

STEP 1

1. The function $g(x) = \sqrt{16 + 2x}$ involves a square root.
2. The domain of the function is determined by the condition that the radicand (the expression inside the square root) must be non-negative.

STEP 2

1. Identify the radicand.
2. Set up the inequality for the radicand to be non-negative.
3. Solve the inequality for $x$ .
4. Express the solution in interval notation.

STEP 3

Identify the radicand of the square root in the function $g(x) = \sqrt{16 + 2x}$ .
The radicand is:
$16 + 2x$

STEP 4

Set up the inequality for the radicand to be non-negative:
$16 + 2x \geq 0$

STEP 5

Solve the inequality $16 + 2x \geq 0$ for $x$ :
Subtract 16 from both sides:
$2x \geq -16$
Divide both sides by 2:
$x \geq -8$

STEP 6

Express the solution in interval notation. Since $x$ must be greater than or equal to $-8$ , the domain of $g(x)$ is:
$[-8, \infty)$
The domain of the function is $\boxed{[-8, \infty)}$ .

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QuestionFind the domain of the function. $g(x)=\sqrt{16+2 x}$
Write your answer using interval notation. \begin{tabular}{|c|} \hline \multirow[t]{3}{*}{(1.ㄴ]} \\ \hline \\ \hline \\ \hline \end{tabular}

Studdy Solution

STEP 1

1. The function $g(x) = \sqrt{16 + 2x}$ involves a square root.
2. The domain of the function is determined by the condition that the radicand (the expression inside the square root) must be non-negative.

STEP 2

1. Identify the radicand.
2. Set up the inequality for the radicand to be non-negative.
3. Solve the inequality for $x$ .
4. Express the solution in interval notation.

STEP 3

Identify the radicand of the square root in the function $g(x) = \sqrt{16 + 2x}$ .
The radicand is:
$16 + 2x$

STEP 4

Set up the inequality for the radicand to be non-negative:
$16 + 2x \geq 0$

STEP 5

Solve the inequality $16 + 2x \geq 0$ for $x$ :
Subtract 16 from both sides:
$2x \geq -16$
Divide both sides by 2:
$x \geq -8$

STEP 6

Express the solution in interval notation. Since $x$ must be greater than or equal to $-8$ , the domain of $g(x)$ is:
$[-8, \infty)$
The domain of the function is $\boxed{[-8, \infty)}$ .

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QuestionFind the domain of the function. g(x)=16+2xg(x)=\sqrt{16+2 x}g(x)=16+2x​Write your answer using interval notation. \begin{tabular}{|c|} \hline \multirow[t]{3}{*}{(1.ㄴ]} \\ \hline \\ \hline \\ \hline \end{tabular}

Studdy Solution

STEP 1

1. The function g(x)=16+2x g(x) = \sqrt{16 + 2x} g(x)=16+2x​ involves a square root.2. The domain of the function is determined by the condition that the radicand (the expression inside the square root) must be non-negative.

STEP 2

1. Identify the radicand.2. Set up the inequality for the radicand to be non-negative.3. Solve the inequality for x x x.4. Express the solution in interval notation.

STEP 3

Identify the radicand of the square root in the function g(x)=16+2x g(x) = \sqrt{16 + 2x} g(x)=16+2x​.The radicand is:16+2x 16 + 2x 16+2x

STEP 4

Set up the inequality for the radicand to be non-negative:16+2x≥0 16 + 2x \geq 0 16+2x≥0

STEP 5

Solve the inequality 16+2x≥0 16 + 2x \geq 0 16+2x≥0 for x x x:Subtract 16 from both sides:2x≥−16 2x \geq -16 2x≥−16Divide both sides by 2:x≥−8 x \geq -8 x≥−8

STEP 6

Express the solution in interval notation. Since x x x must be greater than or equal to −8-8−8, the domain of g(x) g(x) g(x) is:[−8,∞) [-8, \infty) [−8,∞) The domain of the function is [−8,∞) \boxed{[-8, \infty)} [−8,∞)​.

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QuestionFind the domain of the function. $g(x)=\sqrt{16+2 x}$
Write your answer using interval notation. \begin{tabular}{|c|} \hline \multirow[t]{3}{*}{(1.ㄴ]} \\ \hline \\ \hline \\ \hline \end{tabular}

1. The function $g(x) = \sqrt{16 + 2x}$ involves a square root.
2. The domain of the function is determined by the condition that the radicand (the expression inside the square root) must be non-negative.

1. Identify the radicand.
2. Set up the inequality for the radicand to be non-negative.
3. Solve the inequality for $x$ .
4. Express the solution in interval notation.

Identify the radicand of the square root in the function $g(x) = \sqrt{16 + 2x}$ .
The radicand is:
$16 + 2x$

Set up the inequality for the radicand to be non-negative:
$16 + 2x \geq 0$

Solve the inequality $16 + 2x \geq 0$ for $x$ :
Subtract 16 from both sides:
$2x \geq -16$
Divide both sides by 2:
$x \geq -8$

Express the solution in interval notation. Since $x$ must be greater than or equal to $-8$ , the domain of $g(x)$ is:
$[-8, \infty)$
The domain of the function is $\boxed{[-8, \infty)}$ .