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).
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.