The pressure PPP of a gas in a specialized containment unit is modeled as a function of its volume vvv by
P(v)=5v+4v−2,v∈R,v≠2 P(v) = \frac{5v + 4}{v - 2}, \quad v \in \mathbb{R}, v \neq 2 P(v)=v−25v+4,v∈R,v=2The volume VVV of the unit varies with time ttt according to the function
V(t)=9−2t2,t∈R,t≥0 V(t) = 9 - 2t^2, \quad t \in \mathbb{R}, t \ge 0 V(t)=9−2t2,t∈R,t≥0Determine the exact time ttt when the pressure reaching the unit is 3, by solving the equation P(V(t))=3P(V(t)) = 3P(V(t))=3.
Find the inverse function P−1(x)P^{-1}(x)P−1(x).
Sketch and label, on the same axes, the curve with equation y=V(x)y = V(x)y=V(x) and the curve with equation y=V−1(x)y = V^{-1}(x)y=V−1(x). Show on your sketch the coordinates of the points where each curve meets or cuts the coordinate axes.
Practise AQA A Level Maths 1.5 B: Algebra and functions with exam-style questions for A Level Maths. 358 questions 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), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
