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1.5.8 Composite and inverse functions (A-level only)

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Question 39

The concentration of a chemical CCC in a reaction vessel at time ttt minutes is modelled by the function:

C(t)=20−4tfor t≤5 C(t) = \sqrt{20 - 4t} \quad \text{for } t \le 5 C(t)=20−4t​for t≤5

The rate of reaction RRR relative to the concentration is given by:

R(C)=2Cfor C≠0 R(C) = \frac{2}{C} \quad \text{for } C \ne 0 R(C)=C2​for C=0

The overall system function HHH is defined by the composite function H(t)=R(C(t))H(t) = R(C(t))H(t)=R(C(t)) on the maximum possible domain.

a.

Find an expression for H(t)H(t)H(t).

[1]
b.

Find the domain of HHH.

[2]
c.

Show that H−1(x)=5−1x2H^{-1}(x) = 5 - \frac{1}{x^2}H−1(x)=5−x21​.

[3]

1.5.8 Composite and inverse functions (A-level only) Questions

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