Answer
$P^{-1}(t) = -\frac{t+7.5}{2.5}$
Work Step by Step
$P(t) = -2.5t -7.5$
Let $P(t) = y$:
$y = -2.5t - 7.5$.
Switch the variables $t$ and $y$ to find the inverse and solve for $y$:
$t = -2.5y - 7.5$
$t+7.5 = -2.5y$
$y = -\frac{t+7.5}{2.5}$
$P^{-1}(t) = -\frac{t+7.5}{2.5}$.
