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.
471 exam-style questions on Edexcel A Level Maths Functions and Graphs, 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. Each one has a worked solution and a mark scheme showing where the marks go.