### 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 replacing f(x) with y: $y=4-5x$.
Then I swap x and y: $x=4-5y$.
Next, I isolate y by moving the terms involving y to one side and the terms involving x to the other: $5y=4-x$.
Then I divide both sides by 5 to get y by itself: $y=\frac{4-x}{5}$.
This is the inverse of f(x), so I can write it as $f^{-1}(x)=\frac{4-x}{5}$.