### 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, I start by rewriting $f(x)=4-5x$ as $y=4-5x$.
Then, I swap $x$ and $y$ to get $x=4-5y$.
Now, I need to isolate $y$ on one side of the equation.
I can do this by adding $5y$ to both sides and subtracting $x$ from both sides.
This gives me $5y=4-x$.
To finish, I divide both sides by $5$ to get $y=\frac{4-x}{5}$.
This is the inverse function of $f(x)$, so I can write it as $f^{-1}(x)=\frac{4-x}{5}$.