A signal processing unit models the gain G G\,G as a function of input voltage v v\,v according to the rule
G(v)=5−3v2v+1,v∈R,v≠−0.5 G(v) = \frac{5 - 3v}{2v + 1}, \quad v \in \mathbb{R}, v \neq -0.5 G(v)=2v+15−3v,v∈R,v=−0.5The input voltage v v\,v is determined by the time t t\,t in seconds via the function
V(t)=4−2t,t∈R V(t) = 4 - 2t, \quad t \in \mathbb{R} V(t)=4−2t,t∈REvaluate the composite gain GV(−1.5)GV(-1.5)GV(−1.5).
Obtain an expression for the inverse gain function G−1(x)G^{-1}(x)G−1(x).
Determine the values of k k\,k that satisfy the equation G(1k)=V(k+1)\displaystyle G\left(\frac{1}{k}\right) = V(k + 1)G(k1)=V(k+1).
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.
