Step 1 :Let \(f(x)=x+\frac{1}{x}\) and \(g(x)=e^{x}\). We want to find the value of \(f(g(0))\).
Step 2 :First, we need to find the value of \(g(0)\). The function \(g(x)\) is an exponential function with base \(e\). When \(x=0\), \(e^{x}\) equals 1. So, \(g(0)=1\).
Step 3 :Then, we substitute \(g(0)\) into the function \(f(x)\), which is \(f(x)=x+\frac{1}{x}\). So, \(f(g(0))=f(1)=1+\frac{1}{1}=2\).
Step 4 :Final Answer: \(f(g(0))=\boxed{2}\)