Answer:
\(f^{-1}(x)=g(x)=\frac{x-12}{4}\)
Step-by-step explanation:
The problem tell us that \(g(x)\) is the inverse of \(f(x)\), where:
\(f(x)=4x+12\)
So, we need to find the inverse function of \(f(x)\) in order to find \(g(x)\)
Let's find the inverse function using the following steps:
1. Replace \(f(x)\) with \(y\):
\(f(x)=y=4x+12\)
2. Solve the equation for \(x\):
\(\frac{y-12}{4} =x\)
3. Replace every \(x\) with a \(y\) and replace every \(y\) with a \(x\):
\(y=\frac{x-12}{4}\)
4. Finally, replace \(y\) with \(f^{-1}(x)\)
\(f^{-1}(x)=\frac{x-12}{4}\)
Therefore:
\(g(x)=f^{-1}(x)=\frac{x-12}{4}\)
