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.
532 exam-style questions on AQA A Level Maths 1.5 B: Algebra and functions, covering 1.5.1 Laws of indices, 1.5.2 Surds, 1.5.3 Quadratic functions, 1.5.4 Simultaneous equations, 1.5.5 Linear and quadratic inequalities, 1.5.6 Polynomials and rational expressions, 1.5.7 Graphs of functions and proportion, 1.5.8 Composite and inverse functions (A-level only), 1.5.9 Transformations of graphs, 1.5.10 Partial fractions (A-level only), and 1.5.11 Functions in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.