Problem

Let $f(x)=x+\frac{1}{x}$ and $g(x)=e^{x}$. The $f(g(0))=$

Answer

Expert–verified
Hide Steps
Answer

Final Answer: \(f(g(0))=\boxed{2}\)

Steps

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: \(f(g(0))=\boxed{2}\)

link_gpt