In an industrial control system, the output scaling factor, FFF, depends on the input voltage, vvv. The voltage is regulated by a controller setting, sss. The relationship is defined by the following functions:
F(v)=v+3v−2,v∈R,v≠2 F(v) = \frac{v + 3}{v - 2}, \quad v \in \mathbb{R}, v \neq 2 F(v)=v−2v+3,v∈R,v=2 V(s)=2s+1,s∈R V(s) = 2s + 1, \quad s \in \mathbb{R} V(s)=2s+1,s∈RDetermine the output scaling factor when the controller is set to 1.51.51.5, by finding the value of FV(1.5)FV(1.5)FV(1.5).
Derive an expression for the inverse scaling function, F−1(x)F^{-1}(x)F−1(x).
Solve the equation F(1k)=V(k+1)F\left(\frac{1}{k}\right) = V(k + 1)F(k1)=V(k+1) for kkk.
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.