Questions: Determine the implied domain of the following function. Express your answer in interval notation. h(x)=2 sqrt(9-x)

Transcript text: Determine the implied domain of the following function. Express your answer in interval notation. \[ h(x)=2 \sqrt{9-x} \]

Solution

Step 1: Identify the expression under the square root

The expression under the square root is $ax + b$, which is $-x + 9$.

Step 2: Determine the condition for the expression under the square root to be non-negative

Since the square root of a negative number is not defined in the set of real numbers, we require $-x + 9 \geq 0$.

Step 3: Solve the inequality

To find the domain, we solve the inequality $-x + 9 \geq 0$. Given $a = -1$, we solve $x <= \frac{-9}{-1} = 9$.

Step 4: Express the solution in interval notation

Based on the solution to the inequality, the domain in interval notation is $(-∞, 9]$.

The domain of the function $f(x) = \sqrt{-x + 9} + 2$ is $(-∞, 9]$.

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