### 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 write y = 4 - 5x and then swap x and y to get x = 4 - 5y.
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 -(x - 4)/5 = y.
I can simplify this a bit by distributing the negative sign, which gives me (-x + 4)/5 = y.
This is the inverse function, and I can write it as f^-1(x) = (-x + 4)/5.