Question

Find the domain of the function: $ f(x) = \sqrt{7 - 11x} $

• A. \( x \leq \frac{7}{11} \)
• B. \( x \geq \frac{7}{11} \)
• C. \( x \in (-\infty, \infty) \)
• D. \( x \leq -\frac{7}{11} \)

Hint:

When solving for the domain of a square root function, ensure that the radicand (the expression under the square root) is non-negative.

Answer 1

The Correct Option is A

The domain of a function involving a square root requires that the expression inside the square root be non-negative. Therefore, for the function \( f(x) = \sqrt{7 - 11x} \), we need: \[ 7 - 11x \geq 0 \] Solving for \( x \): \[ 7 \geq 11x \] \[ x \leq \frac{7}{11} \]
Thus, the domain of \( f(x) \) is \( x \leq \frac{7}{11} \), which corresponds to option (A).