Find the domain of \( f(x)=\sqrt{2 x+7} \) Use two lower case o's for infinity. "oo" is how you type in infinity.

To find the domain of \( f(x) = \sqrt{2x + 7} \), we need the expression under the square root to be non-negative. This means we require that: \[ 2x + 7 \geq 0 \] Solving this inequality, we subtract 7 from both sides: \[ 2x \geq -7 \] Then, divide by 2: \[ x \geq -\frac{7}{2} \] Thus, the domain of \( f(x) \) is \( \left[-\frac{7}{2}, oo\right) \). Now go ahead and dabble in some more knowledge about square roots! When you're working with square root functions, always remember that the expression inside must be positive or zero—negative numbers are a no-go. Keeping this principle in mind can save you from daunting expressions and ensure your function remains defined and functional! Another interesting aspect of square roots is how they appear in many real-world contexts, like physics and engineering. For instance, the energy of a system can often be linked to square root functions, especially involving calculating distances or forces. When you're dealing with formulas in these fields, watch for those square roots—they're often the key to simplifying complex problems!