# How do you find the minimum value of a square root function f(x)= 3-sqrt(x+2)?

Jun 8, 2015

This one has no minimum value.

As $x$ gets larger, the root gets larger, and the function as a whole becomes more and more negative (slowly but certainly).

Or, in "the language": ${\lim}_{x \to \infty} f \left(x\right) = - \infty$

It does have a maximum though:
The expression under the root may not be negative, it may be $0$. This happens when $x = - 2 \to f \left(x\right) = 3$
graph{3-sqrt(x+2) [-3.85, 47.45, -12.5, 13.2]}

Domain: $x \ge - 2$
Range: $f \left(x\right) \le 3$