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)=20−4tfor t≤5The 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)=C2for C=0The 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.
Find an expression for H(t)H(t)H(t).
Find the domain of HHH.
Show that H−1(x)=5−1x2H^{-1}(x) = 5 - \frac{1}{x^2}H−1(x)=5−x21.
181 exam-style questions on OCR (MEI) A Level Maths 1.3 Functions, covering 1.3.1 Operations on polynomials, 1.3.2 Factor theorem, 1.3.3 Definition of a function (A-level only), 1.3.4 Composite functions (A-level only), 1.3.5 Inverse functions and their graphs (A-level only), 1.3.6 The modulus function (A-level only), 1.3.7 Inequalities with a modulus sign (A-level only), and 1.3.8 Functions in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.