Question 7
Find the inverse of $f(x)=\frac{-3 x-2}{4 x+1}$
\[
f^{-1}(x)=
\]
Question Help: DVideo Message instructor
Submit Question Jump to Answer

Step 1 ：The problem is asking for the inverse of the function \(f(x)=\frac{-3x-2}{4x+1}\).

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 \(y=\frac{-3x-2}{4x+1}\).

Step 4 ：Next, we swap \(x\) and \(y\) to get \(x=\frac{-3y-2}{4y+1}\).

Step 5 ：Now, we solve for \(y\) to get the inverse function. We can do this by multiplying both sides by \(4y+1\) and then adding 2 to both sides and dividing by -3.

Step 6 ：This gives us the inverse function \(f^{-1}(x)=\frac{-4x-2}{3x+1}\).

Step 7 ：\(\boxed{f^{-1}(x)=\frac{-4x-2}{3x+1}}\) is the final answer.