QuestionFind $x$ such that $g(x)=\sqrt{4-x}$ is defined.

Studdy Solution

STEP 1

Assumptions1. The function is $g(x)=\sqrt{4-x}$ . We are looking for all possible values of $x$ that make this function valid3. The square root function is only defined for non-negative numbers

STEP 2

First, we need to set up an inequality that represents the condition under which the square root function is defined. This means the expression under the square root must be greater than or equal to zero.
$4-x \geq0$

STEP 3

Now, we need to solve this inequality for $x$ . We can do this by subtracting $$ from both sides of the inequality.
$-x \geq -$

STEP 4

Next, we multiply both sides of the inequality by $-1$ to isolate $x$ . Remember that when we multiply or divide an inequality by a negative number, we must flip the direction of the inequality.
$x \leq4$

STEP 5

This inequality tells us that $x$ can be any number less than or equal to $4$ .So, the solution is $x \leq4$ .

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QuestionFind $x$ such that $g(x)=\sqrt{4-x}$ is defined.

Studdy Solution

STEP 1

Assumptions1. The function is $g(x)=\sqrt{4-x}$ . We are looking for all possible values of $x$ that make this function valid3. The square root function is only defined for non-negative numbers

STEP 2

First, we need to set up an inequality that represents the condition under which the square root function is defined. This means the expression under the square root must be greater than or equal to zero.
$4-x \geq0$

STEP 3

Now, we need to solve this inequality for $x$ . We can do this by subtracting $$ from both sides of the inequality.
$-x \geq -$

STEP 4

Next, we multiply both sides of the inequality by $-1$ to isolate $x$ . Remember that when we multiply or divide an inequality by a negative number, we must flip the direction of the inequality.
$x \leq4$

STEP 5

This inequality tells us that $x$ can be any number less than or equal to $4$ .So, the solution is $x \leq4$ .

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QuestionFind xxx such that g(x)=4−xg(x)=\sqrt{4-x}g(x)=4−x​ is defined.

Studdy Solution

STEP 1

Assumptions1. The function is g(x)=4−xg(x)=\sqrt{4-x}g(x)=4−x​ . We are looking for all possible values of xxx that make this function valid3. The square root function is only defined for non-negative numbers

STEP 2

First, we need to set up an inequality that represents the condition under which the square root function is defined. This means the expression under the square root must be greater than or equal to zero.4−x≥04-x \geq04−x≥0

STEP 3

Now, we need to solve this inequality for xxx. We can do this by subtracting $$ from both sides of the inequality.−x≥−-x \geq -−x≥−

STEP 4

Next, we multiply both sides of the inequality by −1-1−1 to isolate xxx. Remember that when we multiply or divide an inequality by a negative number, we must flip the direction of the inequality.x≤4x \leq4x≤4

STEP 5

This inequality tells us that xxx can be any number less than or equal to 444.So, the solution is x≤4x \leq4x≤4.

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QuestionFind $x$ such that $g(x)=\sqrt{4-x}$ is defined.

Assumptions1. The function is $g(x)=\sqrt{4-x}$ . We are looking for all possible values of $x$ that make this function valid3. The square root function is only defined for non-negative numbers

First, we need to set up an inequality that represents the condition under which the square root function is defined. This means the expression under the square root must be greater than or equal to zero.
$4-x \geq0$

Now, we need to solve this inequality for $x$ . We can do this by subtracting $$ from both sides of the inequality.
$-x \geq -$

Next, we multiply both sides of the inequality by $-1$ to isolate $x$ . Remember that when we multiply or divide an inequality by a negative number, we must flip the direction of the inequality.
$x \leq4$

This inequality tells us that $x$ can be any number less than or equal to $4$ .So, the solution is $x \leq4$ .