The cooling efficiency, EEE, of a high-performance server rack is modelled by the function
E(v)=5v−2v−4,v>4 E(v) = \frac{5v - 2}{v - 4}, \quad v > 4 E(v)=v−45v−2,v>4where v v\,v is the coolant flow rate in litres per minute.
Use differentiation to show that E E\,E is a decreasing function on its domain.
Find an expression for E−1(v)E^{-1}(v)E−1(v) and state its domain.
Show that the composite function EE(v)EE(v)EE(v) can be written in the form av+bv+c\displaystyle \frac{av + b}{v + c}v+cav+b, where a,b, a, b,\,a,b, and c c\,c are integers to be found.
Deduce the range of EEEEEE.
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.