Question

Let X = {a, b, c} defined by f : X ®X such that f = {(a, b), (b, a), (c,c)}.  Find the values of

f^–1, f² and f⁴

Answer 1

$X = {a,b,c} \\ f={(a,b), (b,a), (c,c)} \\ f(a) = b \\ f(b) = a \\ f(c)=c \\ f^{-1} = {(b,a), (a,b), (c,c)} \\ f^2 = ff(a) =f(b) =a \\ ff(b) = f(a) = b \\ ff(c) =f(c) =c \\ f^2 = {(a,a), (b,b), (c,c)} \\ f^4 = {(a,a), (b,b), (c,c)}$