Write a formula for the function $g(x)$ obtained when the graph of $f(x)=\sqrt{x}$ is shifted up 1 unit and to the left 8 units.

Step 1 ：Given the function \(f(x)=\sqrt{x}\).

Step 2 ：The graph of \(f(x)\) is shifted up 1 unit and to the left 8 units to obtain the function \(g(x)\).

Step 3 ：The formula for the function \(g(x)\) is then \(g(x)=\sqrt{x+8}+1\).

Step 4 ：\(\boxed{g(x)=\sqrt{x+8}+1}\) is the final answer.