Step 1 :Let's find the function \((n \circ m)(x)\).
Step 2 :\((n \circ m)(x)\) represents the composition of functions \(n\) and \(m\).
Step 3 :First, apply \(m(x)\) to \(x\), which gives us \(\sqrt{x+7}\).
Step 4 :Then, apply \(n(x)\) to the result, which gives us \((\sqrt{x+7})+7\).
Step 5 :So, the function \((n \circ m)(x)\) is \(\sqrt{x+7}+7\).
Step 6 :\(\boxed{\sqrt{x+7}+7}\) is the final answer.