### 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 in terms of x.
So first, I'll rewrite the function using y instead of f(x): $y=4-5x$.
Then I'll swap x and y: $x=4-5y$.
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: $\frac{x-4}{-5}=y$.
This is the inverse function, but I can simplify it a bit by distributing the negative sign: $y=-\frac{x}{5}+\frac{4}{5}$.
I can also write it using inverse notation: $f^{-1}(x)=-\frac{x}{5}+\frac{4}{5}$.