The efficiency rating of an industrial turbine, EEE, is modeled as a function of the intake pressure x x\,x by
E(x)=5x+8x−2,x>2 E(x) = \frac{5x + 8}{x - 2}, \quad x > 2 E(x)=x−25x+8,x>2Find an expression for E−1(x)E^{-1}(x)E−1(x).
Show that the composite function EE(x)EE(x)EE(x) can be written in the form
EE(x)=ax+bcx+d EE(x) = \frac{ax + b}{cx + d} EE(x)=cx+dax+bwhere a,b,c a, b, c\,a,b,c and d d\,d are integers to be found.
The point P(6,9.5)P(6, 9.5)P(6,9.5) lies on the curve with equation y=E(x)y = E(x)y=E(x).
Find the coordinates of the point to which P P\,P is mapped when the curve is transformed to y=4E(0.5x)−7y = 4E(0.5x) - 7y=4E(0.5x)−7.
Practise AQA A Level Maths 1.5 B: Algebra and functions with exam-style questions for A Level Maths. 358 questions 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), matched to the AQA A Level Maths (7357) 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.
