QuestionDetermine the domain of the function $q(x)=\sqrt{7-x}$ .

Studdy Solution

STEP 1

Assumptions1. The function is $q(x)=\sqrt{7-x}$ . We are looking for the domain of the function, which is the set of all possible x-values that will make the function defined.

STEP 2

The square root function is only defined for non-negative values. That is, the expression under the square root, $7-x$ , must be greater than or equal to zero.
$7-x \geq0$

STEP 3

To solve this inequality, we first isolate $x$ by subtracting $7$ from both sides.
$-x \geq -7$

STEP 4

Next, we multiply both sides of the inequality by $-1$ . Remember that when we multiply or divide an inequality by a negative number, we must reverse the direction of the inequality.
$x \leq7$

STEP 5

So, the domain of the function $q(x)=\sqrt{7-x}$ is all real numbers $x$ such that $x \leq7$ .
In interval notation, this is written as $(-\infty,7]$ .

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QuestionDetermine the domain of the function $q(x)=\sqrt{7-x}$ .

Studdy Solution

STEP 1

Assumptions1. The function is $q(x)=\sqrt{7-x}$ . We are looking for the domain of the function, which is the set of all possible x-values that will make the function defined.

STEP 2

The square root function is only defined for non-negative values. That is, the expression under the square root, $7-x$ , must be greater than or equal to zero.
$7-x \geq0$

STEP 3

To solve this inequality, we first isolate $x$ by subtracting $7$ from both sides.
$-x \geq -7$

STEP 4

Next, we multiply both sides of the inequality by $-1$ . Remember that when we multiply or divide an inequality by a negative number, we must reverse the direction of the inequality.
$x \leq7$

STEP 5

So, the domain of the function $q(x)=\sqrt{7-x}$ is all real numbers $x$ such that $x \leq7$ .
In interval notation, this is written as $(-\infty,7]$ .

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QuestionDetermine the domain of the function q(x)=7−xq(x)=\sqrt{7-x}q(x)=7−x​.

Studdy Solution

STEP 1

Assumptions1. The function is q(x)=7−xq(x)=\sqrt{7-x}q(x)=7−x​ . We are looking for the domain of the function, which is the set of all possible x-values that will make the function defined.

STEP 2

The square root function is only defined for non-negative values. That is, the expression under the square root, 7−x7-x7−x, must be greater than or equal to zero.7−x≥07-x \geq07−x≥0

STEP 3

To solve this inequality, we first isolate xxx by subtracting 777 from both sides.−x≥−7-x \geq -7−x≥−7

STEP 4

Next, we multiply both sides of the inequality by −1-1−1. Remember that when we multiply or divide an inequality by a negative number, we must reverse the direction of the inequality.x≤7x \leq7x≤7

STEP 5

So, the domain of the function q(x)=7−xq(x)=\sqrt{7-x}q(x)=7−x​ is all real numbers xxx such that x≤7x \leq7x≤7.In interval notation, this is written as (−∞,7](-\infty,7](−∞,7].

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QuestionDetermine the domain of the function $q(x)=\sqrt{7-x}$ .

Assumptions1. The function is $q(x)=\sqrt{7-x}$ . We are looking for the domain of the function, which is the set of all possible x-values that will make the function defined.

The square root function is only defined for non-negative values. That is, the expression under the square root, $7-x$ , must be greater than or equal to zero.
$7-x \geq0$

To solve this inequality, we first isolate $x$ by subtracting $7$ from both sides.
$-x \geq -7$

Next, we multiply both sides of the inequality by $-1$ . Remember that when we multiply or divide an inequality by a negative number, we must reverse the direction of the inequality.
$x \leq7$

So, the domain of the function $q(x)=\sqrt{7-x}$ is all real numbers $x$ such that $x \leq7$ .
In interval notation, this is written as $(-\infty,7]$ .