If `A={1,2,3},B=(alpha,beta,gamma),c=(p,q,r) and (f:A to B,g:B to C` are defined by `f={(1,alpha),(2,gamma),(3,beta)},g={(alpha,q),(gamma,p)}` then show that f and g are bijective functions and `(gof)^(-1)=f^(-1)og^(-1).`

Let A={1,2,3},B={a,b,c),C={p,q,r}. If f:A to B, g: B to C are defined by f={(1,a),(2,c),(3,b)},g={a,q),(b,r),(c,p)} then show that f^(-1)og^(-1)=(gof)^(-1) .

If f:ArarrB,g:BrarrC are two bijective functions then P.T ("gof")^(-1)=f^(-1)"og"^(-1)

Let f={(1,a),(2,c),(4,d),(3,b)} and g^(-1) = {(2,a),(4,b),(1,c),(3,d)} then show that (gof)^(-1) = f^(-1) og^(-1) .

If alpha, beta, gamma are the roots of x^(3)+px+q=0 then |(alpha, beta, gamma),(beta, gamma, alpha),(gamma, alpha, beta)|=

Consider f: {1,2,3} to {a,b,c} and g: {a,b,c} to {apple, ball, cat} defined as f (1) =a, f (2) =b, f (3)=c, g (a) = apple, g (b) = ball and g (c )= cat. Show that f, g and gof are invertible. Find out f ^(-1) , g ^(-1) and ("gof")^(-1) and show that ("gof") ^(-1) =f ^(-1) og ^(-1).