find the domain of each expression

-15 multiplied by square root of x+2

1 answer

To find the domain of the expression \(-15 \cdot \sqrt{x + 2}\), we need to determine the set of values for \(x\) for which the expression is defined.

The square root function is defined only for non-negative values. Thus, we need the expression inside the square root to be greater than or equal to zero:

\[ x + 2 \geq 0 \]

Now, we can solve this inequality:

\[ x \geq -2 \]

Therefore, the domain of the expression \(-15 \cdot \sqrt{x + 2}\) is:

\[ [-2, \infty) \]

This means that \(x\) can take any value from \(-2\) to positive infinity, inclusive of \(-2\).