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≠−0.5G(v) = \frac{5 - 3v}{2v + 1}, \quad v \in \mathbb{R}, v \neq -0.5G(v)=2v+15−3v,v∈R,v=−0.5 The input voltage v v\,v is determined by the time t t\,t in seconds via the function V(t)=4−2t,t∈RV(t) = 4 - 2t, \quad t \in \mathbb{R}V(t)=4−2t,t∈R
Evaluate 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 Edexcel A Level Maths Functions and Graphs with exam-style questions for A Level Maths. 100 questions covering 2.1 The Modulus Function, 2.2 Functions and Mappings, 2.3 Composite Functions, 2.4 Inverse Functions, 2.5 y=|f(x)| and y=f(|x|), 2.6 Combining Transformations, and 2.7 Solving Modulus Problems, matched to the Edexcel A Level Maths (9MA0) 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.