Questions: Find the domain of the function. g(x)=sqrt(4-x) The domain of g(x)=sqrt(4-x) is . (Type your answer in interval notation.)

Transcript text: Find the domain of the function. \[ g(x)=\sqrt{4-x} \] The domain of $g(x)=\sqrt{4-x}$ is $\square$ . (Type your answer in interval notation.)

Solution

Solution Steps

Step 1: Identify the expression inside the square root

The expression inside the square root is $a - bx$, where $a = 4$ and $b = 1$.

Step 2: Set the expression inside the square root greater than or equal to 0

For the square root to be real and defined, we set $a - bx \geq 0$, which simplifies to $ 4 - x >= 0 $.

Step 3: Solve the inequality

Since $b > 0$, we solve the inequality $a - bx \geq 0$ for $x$, leading to $x \leq \frac{a}{b} = 4$.

Step 4: Express the domain in interval notation

Based on the solution to the inequality, the domain of the function in interval notation is (-∞, 4].

Final Answer:

The domain of the function $g(x) = \sqrt{4 - x}$ is (-∞, 4].

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