Questions: Find the domain of the function. h(x) = sqrt(-4x + 32) Write your answer using interval notation.

Transcript text: Find the domain of the function. \[ h(x)=\sqrt{-4 x+32} \] Write your answer using interval notation.

Solution

Solution Steps

Step 1: Identify the expression under the square root

The function \( h(x) = \sqrt{-4x + 32} \) contains a square root. For the square root to be defined in real numbers, the expression inside the square root must be non-negative. Therefore, we set up the inequality: \[ -4x + 32 \geq 0 \]

Step 2: Solve the inequality for \( x \)

Solve the inequality \( -4x + 32 \geq 0 \) for \( x \): \[ -4x + 32 \geq 0 \\ -4x \geq -32 \\ x \leq 8 \] (Note: When dividing or multiplying both sides of an inequality by a negative number, the inequality sign reverses.)

Step 3: Write the domain in interval notation

The solution \( x \leq 8 \) means that the domain of \( h(x) \) is all real numbers less than or equal to 8. In interval notation, this is written as: \[ (-\infty, 8] \]

Final Answer

\(\boxed{(-\infty, 8]}\)

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >

Thank you for your feedback.

Copied!