Show $f(x)=3-4 x$ and $g(x)=\frac{3-x}{4}$ are inverse functions.

Step 1 ：We are given two functions, \(f(x) = 3 - 4x\) and \(g(x) = \frac{3 - x}{4}\).

Step 2 ：To prove that these two functions are inverses of each other, we need to show that the composition of the two functions in both orders results in the identity function.

Step 3 ：In other words, we need to show that \(f(g(x)) = x\) and \(g(f(x)) = x\).

Step 4 ：Let's start by finding \(f(g(x))\). Substituting \(g(x)\) into \(f(x)\), we get \(f(g(x)) = 3 - 4(\frac{3 - x}{4}) = x\).

Step 5 ：Next, let's find \(g(f(x))\). Substituting \(f(x)\) into \(g(x)\), we get \(g(f(x)) = \frac{3 - (3 - 4x)}{4} = x\).

Step 6 ：Since both \(f(g(x)) = x\) and \(g(f(x)) = x\), we can conclude that \(f(x)\) and \(g(x)\) are indeed inverse functions of each other.

Step 7 ：\(\boxed{f(x)\) and \(g(x)\) are inverse functions.}