Question

(x)). For each pair of functions f and g below, find f(g(x)) and g Then, determine whether f and g are inverses of each other. Simplify your answers as much as possible. (Assume that your expressions are defined for all x in the domain of the composition. You do not have to indicate the domain.) (a) f(x) = x + 4 (b) f(x) = - -, 0 3x x 5 ? g(x) = x - 4 f(g(x)) = 0 8(x) = *,*+0 $(g(x)) = 0 g['(x)) = 0 g(x)) = 0 of and g are inverses of each other fand g are inverses of each other f and g are not inverses of each other fand g are not inverses of each other

Answer 1

foa) and ga) are ioverses of each otner Then fCoa) - 9 Cfa))= Ca) Let fx) = a+4 and 9Cx)=-4 Then f(gx)) =f(a-4) =a-4)+4a 7 an d 9cfn) = 9 (x + 4) -+ 4)-4 -a Thus, f(9)) 9(fCa)) fand 9 e inverses of each other. and gca) 3a Cb) Let fa) fo o Then f(9a) f Caa 3(3 and gcfca)) 9) 3 since f(9a)) - 9Cfa))f and g ae inverses of each other,