The function f(x) = log3(x - 2) - 1 has an inverse function f (x). (a) State the domain and range of the function f (x) . ( b ) Find the rule of the inverse function f (x) , and state also its domain and range. MUFY@SC Pathway to a Brighter Future Page 64 of 149@3395?" 33 33 2: no 332an ha ~23 >335 .323 move mo "8 "Ea 2: 8 3 7x 23 3x 8 mo 39an ea ea E l.|||||.l||l|:||.|l_ NgsBmlbzig ma, , MATHS UNIT 1 - STUDY AREA 2 2023 Question 6 The population of a species of water beetle was observed over an eight-week period. The algebraic model used to describe the population was P(t) = 5000 + 2000 sin () where P(t) stands for the population after t weeks, te [0,8]. (a) State the period of this function. (b ) State the maximum and minimum population size during the 8 weeks. (c) Find all the values of t where the population reached 6000 beetles. (d) Find the population size of the water beetles, 4 weeks into the observed period. Give your answer correct to the nearest whole number. (e ) Sketch the graph of P(t) against t for 0