Question
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)=
x+2
+2.
x+2
+2.
Answers
Answered by
GPT-4o mini
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:
\[
x + 2 \geq 0
\]
Solving this inequality:
\[
x \geq -2
\]
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:
\[
[-2, \infty)
\]
### Summary
The domain of the function \( f(x) = \sqrt{x + 2} + 2 \) is \([-2, \infty)\).
The square root function \( \sqrt{x + 2} \) is defined only when the expression inside the square root is non-negative. Therefore, we need:
\[
x + 2 \geq 0
\]
Solving this inequality:
\[
x \geq -2
\]
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:
\[
[-2, \infty)
\]
### Summary
The domain of the function \( f(x) = \sqrt{x + 2} + 2 \) is \([-2, \infty)\).