Answer
(a) $f^{-1}(p)=\frac{150-p}{3}$
The inverse function represents the price of commodity for given amount demand.
(b) $f^{-1}(30)=40$
It represents price, which is $40$ for the amount demand of $30$.
Work Step by Step
$f(p)=-3p+150$
(a) To find $f^{-1}$ we will follow the next steps:
First write the expression in terms of $y$ and $p$:
$y=-3p+150$
Then replace $y$ by $x$ and vice versa:
$p=-3y+150$
And solve it for $y$:
$3y=150-p$
$y=\frac{150-p}{3}$
$f^{-1}(p)=\frac{150-p}{3}$
It represents the price of commodity for given demand.
(b)
$f^{-1}(30) = \frac{150-30}{3}=\frac{120}{3}=40$
$f^{-1}(30)=40$ And it represents price, which is $40$ for the demand of $30$.
