If we have two functions, \(f(x)=\sqrt{x}\) and \(g(x)=2x+3\), what is the domain of the composite function \(f(g(x))\)?

Step 1 ：The domain of a function is the set of all possible input values (x-values) that will return a real number.

Step 2 ：Let's first look at the function \(g(x)\). Its domain is all real numbers, because any real number can be plugged into \(x\) to obtain a real number.

Step 3 ：Now, let's look at the composite function \(f(g(x))\). This means that we're plugging \(g(x)\) into \(f(x)\). So, we get \(f(g(x)) = \sqrt{2x+3}\).

Step 4 ：The square root function is only defined for non-negative numbers. So, we need to find the values of \(x\) such that \(2x+3 \geq 0\).

Step 5 ：Solving the inequality \(2x+3 \geq 0\), we get \(x \geq -\frac{3}{2}\).