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10., , 11., , 12., , Miscellaneous Exercise on Chapter 2, , x 0<x<3, , ation Fisdeh (x) =, The relation fis defined by f (oes, , x ,O0<x<2, , ion vis-defi ()=, The relation g is defined by & { 2<x<10, , Show that fis a function and g is not a function., , 2 fAD-fO, . if =x, find ——_———_., f(x) =x, fin (=), 2, x #2x+1, Find the domain of the function f(x) =—3————__, x -8x+12, , Find the domain and the range of the real function f defined by f(x) = /(x-1) ., , Find the domain and the range of the real function f defined by f (x) = |x-1]., , 2, x, Let f= {(s} xe x| be a function from R into R. Determine the range, , of f., , . Let f, g : ROR be defined, respectively by f(x) = x + 1, g(x) = 2x — 3. Find, , + mt, f +8 f-g an g°, , Let f= {(1,]), (2,3), (0-1), (-1, -3)} be a function from Z to Z defined by, , J(x) = ax + b, for some integers a, b. Determine a, b., , Let R be a relation from N to N defined by R = {(a, b): a,b EN anda= Db}. Are, the following true?, (i) (aa) € R, forallae N (ii) (a,b) € R, implies (b,a) € R, (iii) (a,b) € R, (b,c) € R implies (a,c) € R., Justify your answer in each case., Let A={1,2,3,4}, B= {1,5,9,11,15,16} and f= {(1,5), (2,9), (3,1), (4,5), (2,11)}, Are the following true?, (i) fis a relation from A to B (i) f is a function from A to B., Justify your answer in each case., , 2020-21, , RELATIONS AND FUNCTIONS 47, , Let f be the subset of Z x Z defined by f = {(ab,a+b):a,be€ Z}.Isfa, function from Z to Z? Justify your answer., , Let A= {9,10,11,12,13} and let f: AN be defined by f (1) = the highest prime, factor of n. Find the range of f.