### 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 first, I write $y=4-5x$ and then I replace x with y and y with x: $x=4-5y$.
Now, I need to isolate y on one side of the equation.
I can start by subtracting 4 from both sides: $x-4=-5y$.
Then I can divide both sides by -5 to get y by itself: $y=\frac{x-4}{-5}$.
This is the inverse function of f(x), but I can simplify it a bit more by distributing the negative sign in the denominator: $y=-\frac{x}{5}+\frac{4}{5}$.
So the inverse of f(x) is $f^{-1}(x)=-\frac{x}{5}+\frac{4}{5}$.