at what points is the following function continuous? f(x) = \\sqrt{6x + 7} the set of x - values where the…

at what points is the following function continuous? f(x) = \\sqrt{6x + 7} the set of x - values where the function is continuous is (simplify your answer. type your answer in interval notation.)

at what points is the following function continuous? f(x) = \\sqrt{6x + 7} the set of x - values where the function is continuous is (simplify your answer. type your answer in interval notation.)

Answer

Explanation:

Step1: Recall continuity condition for square - root functions

For $y = \sqrt{u}$, $u\geq0$. Here $u = 6x + 7$.

Step2: Set up the inequality

We set $6x+7\geq0$.

Step3: Solve the inequality for $x$

Subtract 7 from both sides: $6x\geq - 7$. Then divide by 6: $x\geq-\frac{7}{6}$.

Answer:

$\left[-\frac{7}{6},\infty\right)$