find the domain of each expression

15- multiplied by square root of x+2

1 answer

To find the domain of the expression \( 15 - \sqrt{x + 2} \), we need to consider the requirements for the square root to be defined.

  1. The expression under the square root, \( x + 2 \), must be non-negative: \[ x + 2 \geq 0 \] This simplifies to: \[ x \geq -2 \]

Since there are no other restrictions on \( x \), the domain of the expression \( 15 - \sqrt{x + 2} \) is:

\[ \text{Domain: } [-2, \infty) \]

This means that \( x \) can take any value from \(-2\) to \(\infty\) (including \(-2\)).