Use graphing technology to find the domain of the function f, of, x, equals, square root of, x, plus, 2, end square root, plus, 2, .f(x)=

Question

x+2
​
+2.

Answer 1

To find the domain of the function $f(x)=\sqrt{x+2}+2$, we need to determine the values of $x$ for which the function is defined.

The square root function $\sqrt{x+2}$ is defined only when the expression inside the square root is non-negative. Therefore, we need:

$$x+2\ge 0$$

Solving this inequality:

$$x\ge -2$$

Thus, the domain of the function $f(x)=\sqrt{x+2}+2$ is all values of $x$ greater than or equal to $-2$. In interval notation, the domain is:

$$[-2,\mathrm{\infty })$$

Summary

The domain of the function $f(x)=\sqrt{x+2}+2$ is $[-2,\mathrm{\infty })$.