Answer
a) $f^{-1}=-(D-150)/3$.
b) $\$40/unit$
Work Step by Step
a) If we want to get a formula for the inverse function, we swap $x$ and $y$ and solve for $y$.
Hence, after swapping $x$ and $y$, we get:
$x=-3y+150\\x-150=-3y\\y=f^{-1}=-(D-150)/3$
This represents the price associated with the demand $D$.
b) Plugging in $30$ into the inverse function above, we get: $40$. Thus, when the demand is $30$ units, the price is $\$40/unit$.
