Find the inverse of the following function.
\[
f(x)=7 x^{2}+4 \quad x \geq 0
\]
Provide your answer below:
\[
f^{-1}(x)=
\]

Step 1 ：The problem is asking for the inverse of the function \(f(x)=7x^{2}+4\) where \(x \geq 0\).

Step 2 ：To find the inverse of a function, we need to switch the roles of \(x\) and \(y\) and solve for \(y\).

Step 3 ：Let's start by replacing \(f(x)\) with \(y\), so we have \(y=7x^{2}+4\).

Step 4 ：Next, we swap \(x\) and \(y\) to get \(x=7y^{2}+4\).

Step 5 ：Now, we solve for \(y\) to get the inverse function. We can do this by subtracting 4 from both sides and then dividing by 7.

Step 6 ：This gives us \(y^{2}=(x-4)/7\). Since \(x \geq 0\), we take the positive square root to get \(y=\sqrt{(x-4)/7}\).

Step 7 ：\(\boxed{f^{-1}(x)=\sqrt{(x-4)/7}}\) is the final answer.