For each of the following functions: (i) determine their natural domain; (ii) find a formula for the inverse (if it exists may require restriction of domain); (iii) determine the range of both the function and its inverse. (a) f(x)= (b) g(x)= = 2x+1 2-3 1-e 1+ e* 1 (c) h(x)= 9 - 3x (d) m(x) = 1-3 ln(2 - 3x) Some less-standard functions. (a) Let f: {People} Z be defined by f(x) = the number of hairs on a's head. Is f surjective? (b) Let f: {People} {People} be defined by f(2)= the mother of r. Is f well defined? Is f surjective? Is f injective? (c) Let f: (People currently enrolled in MTH1020} {Days of the year} be defined by f(x)=r's birthday. Is f injective? You can assume there are at least 400 people currently enrolled in MTH1020. (d) Let f: (1901, 1902,... 2000} {People} be defined by f(t) is the Prime Minister of Australia on January 1 in year t. Is f injective? Is f surjective? For each of the following functions: (i) determine their natural domain; (ii) find a formula for the inverse (if it exists may require restriction of domain); (iii) determine the range of both the function and its inverse. (a) f(x)= (b) g(x)= = 2x+1 2-3 1-e 1+ e* 1 (c) h(x)= 9 - 3x (d) m(x) = 1-3 ln(2 - 3x) Some less-standard functions. (a) Let f: {People} Z be defined by f(x) = the number of hairs on a's head. Is f surjective? (b) Let f: {People} {People} be defined by f(x) = the mother of r. Is f well defined? Is f surjective? Is f injective? (c) Let f: (People currently enrolled in MTH1020} {Days of the year} be defined by f(x) = x's birthday. Is f injective? You can assume there are at least 400 people currently enrolled in MTH1020. (d) Let f: (1901, 1902,... 2000} {People} be defined by f(t) is the Prime Minister of Australia on January 1 in year t. Is f injective? Is f surjective?