page 06 MARKS 8. A function, f, is given by ( ) 3 8 f x x = + . The domain of f is , 1 1000 x x ≤ ≤ ∈\ . The inverse function, f -1, exists. (a) Find ( ) 1 f x − . (b) State the domain of f -1. 9. Electricity on a spacecraft can be produced by a type of nuclear generator. The electrical power produced by this generator can be modelled by · 0 0079 120 t tP e− = where Pt is the electrical power produced, in watts, after t years. (a) Determine the electrical power initially produced by the generator. (b) Calculate how long it takes for the electrical power produced by the generator to reduce by 15%. 10. (a) Show that ( ) 3 x + is a factor of 4 3 2 3 10 8 6 x x x x + + − −. (b) Hence, or otherwise, factorise 4 3 2 3 10 8 6 x x x x + + − − fully. 3 1 1 4 2 5