Discussion
The domain of the function \(f(x) = \sqrt{7 - 11x}\) is
Answer: C
The domain is \(\left(-\infty, \frac{7}{11}\right]\).
A square root is real only when its argument is non-negative:
\[ 7 - 11x \ge 0 \;\Rightarrow\; x \le \frac{7}{11} \]
So every \(x\) up to and including \(7/11\) is allowed. \(\left[\frac{7}{11}, \infty\right)\) reverses the inequality (the sign flips only when dividing by a negative number, which is not done here), and \((-\infty, -1]\), \(\left[\frac{7}{11}, 1\right]\) and \([-1, 1]\) are only parts of the domain or lie outside it.
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