The power output, PPP, of a prototype turbine is modeled by the function
P(t)=15(t2+6),t≥0 P(t) = \frac{1}{5}(t^2 + 6), \quad t \ge 0 P(t)=51(t2+6),t≥0where ttt is the time in hours since activation.
Find the range of PPP.
Find P−1(t)P^{-1}(t)P−1(t).
State the range of P−1(t)P^{-1}(t)P−1(t).
State the geometric transformation which maps the graph of y=P(t)y = P(t)y=P(t) onto the graph of y=P−1(t)y = P^{-1}(t)y=P−1(t).
Find the coordinates of the points of intersection of the graphs of y=P(t)y = P(t)y=P(t) and y=P−1(t)y = P^{-1}(t)y=P−1(t).
181 exam-style questions on OCR (MEI) A Level Maths 1.3 Functions, covering 1.3.1 Operations on polynomials, 1.3.2 Factor theorem, 1.3.3 Definition of a function (A-level only), 1.3.4 Composite functions (A-level only), 1.3.5 Inverse functions and their graphs (A-level only), 1.3.6 The modulus function (A-level only), 1.3.7 Inequalities with a modulus sign (A-level only), and 1.3.8 Functions in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.