Questions: Determine the domain for the following square root function. f(x)=-√(-10x+6) x ≤ 0.6 Round your answer to three decimal places if necessary.

Solution Steps

To determine the domain of the square root function \( f(x) = -\sqrt{-10x + 6} \), we need to ensure that the expression inside the square root is non-negative. This means solving the inequality \(-10x + 6 \geq 0\). Once we find the range of \( x \) that satisfies this inequality, we can determine the domain of the function.

To find the domain of the function \( f(x) = -\sqrt{-10x + 6} \), we need to ensure that the expression inside the square root is non-negative: \[ -10x + 6 \geq 0 \]

Rearranging the inequality gives: \[ 6 \geq 10x \] Dividing both sides by 10 results in: \[ \frac{6}{10} \geq x \quad \text{or} \quad x \leq \frac{3}{5} \]

The solution to the inequality indicates that \( x \) can take any value less than or equal to \( \frac{3}{5} \). Therefore, the domain of the function is: \[ (-\infty, \frac{3}{5}] \]

Final Answer