Find the domain of the function. (Enter your answer using interval notation.)f(x) = log2(x + 3)

1. Break Down the Problem

To find the domain of the function $f(x) = \log_2(x + 3)$, we need to determine for which values of $x$ the logarithm is defined.

2. Relevant Concepts

The logarithmic function $\log_b(x)$ is defined only for positive values of $x$. Therefore, we need to find when the argument of the logarithm $x + 3$ is greater than zero:

$x + 3 > 0$

3. Analysis and Detail

We can solve the inequality:

$x + 3 > 0$ $x > -3$

This tells us that $x$ must be greater than -3.

4. Verify and Summarize

To express the domain in interval notation, we note that $x$ can take any value greater than -3, extending to positive infinity. Thus, the domain in interval notation is:

$(-3, \infty)$

Final Answer

The domain of the function $f(x) = \log_2(x + 3)$ is $(-3, \infty)$.