Describing Inverses of Functions

The first step is to determine the function's inverse. To find the inverse of the function, we will first switch $x$ and $y.$ $$\begin{array}{c}y=4-3x\stackrel{\text{switch}}{⟶}x=4-3y\end{array}$$ Now, we will isolate the $y\text{-}$variable. The result will be the inverse of the given function. Now that we found the inverse of the function, we can determine whether it represents a function. $$\begin{array}{c}y=\frac{4-x}{3}\end{array}$$ A function is a relation where each input is related to exactly one output. In this case, for each $x$ in domain of the inverse, there is only one value of $y$ in the range. Therefore, the inverse is a function in its domain. The function is invertible.