The profit function ppp for a project and the efficiency function qqq are defined by
p(t)=81−t2t∈R,t≥0p(t) = 81 - t^2 \quad t \in \mathbb{R}, t \ge 0p(t)=81−t2t∈R,t≥0 q(v)=125v+2v∈R,v≥0q(v) = \frac{12}{5v + 2} \quad v \in \mathbb{R}, v \ge 0q(v)=5v+212v∈R,v≥0
Determine the range of the function ppp.
Calculate the value of pq(0.2)pq(0.2)pq(0.2).
Determine the inverse function q−1(x)q^{-1}(x)q−1(x) and state its domain.