### Instruction: What is the inverse of $f(x)=4-5x$?### Response: To find the inverse of a function, I need to switch the roles of $x$ and $y$ and then solve for $y$.
So, if $y=4-5x$, then $x=4-5y$ after switching $x$ and $y$.
Now, I need to isolate $y$ on one side of the equation.
I can start by subtracting $4$ from both sides, which gives me $x-4=-5y$.
Then, I can divide both sides by $-5$, which gives me $-\frac{x}{5}+\frac{4}{5}=y$.
This is the inverse function of $f(x)$, but I can also write it in function notation as $f^{-1}(x)=-\frac{x}{5}+\frac{4}{5}$.