If `f={(1,a), (2, b), (1, b), (3,c), (1,c)}, g=(a, p), (b,r), (c,q), (c,p)}`, then `(gof)^(-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 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=[{:(a,b,c),(p,q,r),(1,1,1):}]and B=A^(2) If (a-b)^(2) +(p-q)^(2) =25, (b-c) ^(2)+ (q-r)^(2)= 36 and (c-a)^(2) +(r-p)^(2)=49, then det B is

If A = {p,q,r, s} and B = {1, 2, 3} , find which of the following is not a function from A to B? A. R_1={(p,1),(q,2),(r,1),(s,2)} B. R_2={(p,1),(q,1),(r,1),(s,1)} C. R_3={(p,1),(q,2),(p,2),(s,3)} D. R_4={(p,2),(q,3),(r,2),(s,2)} ANSWER: C

If a !=p, b !=q, c!=r and |(p,b,c),(a,q,c),(a,b,r)| = 0 then the value of (p)/(p-a)+(q)/(q-b)+(r)/(r-c) is equal to a)-1 b)1 c)-2 d)2

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

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).