How many functions are possible from the set `A={1,2,3}` in to itselt if `f(1)!=1,f(2)!=2` and `f(3)!=3`.

How many of the following are possible 1p,2s,3p,3f,3d

How many of the following are possible 1p,2s,3p,3f,3d

The total number of function f from the set (1,2,3) into the set (1,2,3,4,5) such that f(i)<=f(j)AA i

Let the set S={f_(1),f_(2),f_(3),f_(4)} of four functions from CC (the set of all complex numbers) to itself, defined by f_(1)(z)=z,f_(2)(z)=-z,f_(3)(z)=(1)/(z)andf_(4)(z)=-(1)/(z) for all zinCC Construct the composition table for the composition of functions (@) defined on the set S. value of f_(2)@f_(1)(z) is--

Let the set S={f_(1),f_(2),f_(3),f_(4)} of four functions from CC (the set of all complex numbers) to itself, defined by f_(1)(z)=z,f_(2)(z)=-z,f_(3)(z)=(1)/(z)andf_(4)(z)=-(1)/(z) for all zinCC Construct the composition table for the composition of functions (@) defined on the set S. Value of f_(2)@f_(4)(z) is---

Let the set S={f_(1),f_(2),f_(3),f_(4)} of four functions from CC (the set of all complex numbers) to itself, defined by f_(1)(z)=z,f_(2)(z)=-z,f_(3)(z)=(1)/(z)andf_(4)(z)=-(1)/(z) for all zinCC Construct the composition table for the composition of functions (@) defined on the set S. Value of f_(4)@f_(1)(z) is ---

If the function f={(1,5),(2,6),(3,4)} from the set A={1,2,3} to the set B is invertible find the set B.

Consider the set A={1,2,3,4,5} , and B={1,4,9,16,25} and a function f:AtoB defined by f(1)=1 , f(2)=4 , f(3)=9 , f(4)=16 and f(5)=25 . Does f^-1 exists? Explain.