Find the domain of \( f \) and write your answer in interval notation. \( f(x)=8 \sqrt{5-7 x}+6 \) Question Help: Video Submit Question

To find the domain of \( f(x) = 8 \sqrt{5 - 7x} + 6 \), we need to determine where the expression under the square root is non-negative because you cannot take the square root of a negative number. So, we set up the inequality: \[ 5 - 7x \geq 0 \] Solving this gives: \[ 5 \geq 7x \] \[ \frac{5}{7} \geq x \] This means \( x \) must be less than or equal to \( \frac{5}{7} \). Since there are no restrictions on how small \( x \) can get (it can go to negative infinity), our domain in interval notation is: \[ (-\infty, \frac{5}{7}] \]