### Instruction: What is the inverse of $f(x)=4-5x$?### Response: To find the inverse of a function, I need to swap the roles of x and y and then solve for y in terms of x.
So first, I will rewrite $f(x)=4-5x$ as $y=4-5x$.
Then, I will switch 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, which gives me $x+5y=4$.
Then, I can subtract x from both sides, which gives me $5y=4-x$.
Finally, I can divide both sides by 5, which gives me $y=\frac{4-x}{5}$.
This is the inverse function of $f(x)=4-5x$, so I can write it as $f^{-1}(x)=\frac{4-x}{5}$.