We need to find the interval of continuity for the function $f(x) = \frac{1}{\sqrt{x+10}}$.

1. Problem Description

We need to find the interval of continuity for the function $f(x) = \frac{1}{\sqrt{x+10}}$.

2. Solution Steps

For the function $f(x) = \frac{1}{\sqrt{x+10}}$ to be continuous, the expression inside the square root must be strictly greater than zero, because we cannot take the square root of a negative number, and the denominator cannot be zero.

Thus, we need to find the values of $x$ such that $x + 10 > 0$.

$x + 10 > 0$

$x > -10$

So the function is continuous for all $x$ greater than $-10$. In interval notation, this is $(-10, \infty)$.

3. Final Answer

The interval of continuity is $(-10, \infty)$. The correct answer is B.