The net harvesting efficiency EEE of a solar panel array over time ttt (in years) is modeled by the function:
E(t)=3−t−2t+4+t+702t2+5t−12,t>4 E(t) = 3 - \frac{t - 2}{t + 4} + \frac{t + 70}{2t^2 + 5t - 12}, \quad t > 4 E(t)=3−t+4t−2+2t2+5t−12t+70,t>4Show that
E(t)=at+bct+d,t>4 E(t) = \frac{at + b}{ct + d}, \quad t > 4 E(t)=ct+dat+b,t>4where a,b,ca, b, ca,b,c and ddd are integers to be found.
Determine an expression for E−1(x)E^{-1}(x)E−1(x).
Find the domain of E−1E^{-1}E−1.
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.