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

Given the function \(f(x) = 3x + 4\), we switch \(x\) and \(y\) and solve for \(x\):

x = 3y + 4.\)

Now, solve for \(y\):

3y = x - 4.\)

Divide both sides by \(3\):

y = \frac{x - 4}{3}.\)

So, the inverse function of \(f(x) = 3x + 4\) is \(\frac{x - 4}{3}\).