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3.1.5 Algebra and functions (A-level only)

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Question 22

The profit function ppp for a project and the efficiency function qqq are defined by

p(t)=81−t2t∈R,t≥0 p(t) = 81 - t^2 \quad t \in \mathbb{R}, t \ge 0 p(t)=81−t2t∈R,t≥0 q(v)=125v+2v∈R,v≥0 q(v) = \frac{12}{5v + 2} \quad v \in \mathbb{R}, v \ge 0 q(v)=5v+212​v∈R,v≥0
a.

Determine the range of the function ppp.

[1]
b.

Calculate the value of pq(0.2)pq(0.2)pq(0.2).

[2]
c.

Determine the inverse function q−1(x)q^{-1}(x)q−1(x) and state its domain.

[4]

3.1.5 Algebra and functions (A-level only) Questions

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