Let `f={(1,1),(2,3),(0,−1),(−1,−3)}` be a function from Z to Z defined by `f(x)=ax+b` for some integers a,b. Determine `a,b.`

Let f={(1,1),(2,3),(0,-1),(,-1,-3)} be a linear function from Z into Z. Find f(x).

Let a function f:(0,infty)to[0,infty) be defined by f(x)=abs(1-1/x) . Then f is

If the function f be defined by f(x) =(2x +1)/(1-3x) , then f ^(-1) (x) is-

Find the inverse of the function: f:Z to Z defined by f(x)=[x+1], where [.] denotes the greatest integer function.

let A =RR-{-(1)/(2)} and B=RR -{(1)/(2)} . Prove that function f: A rarr B define by , f(x)=(x+2)/(2x+1) is invertible and hence find f^(-1) (x)

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_(4)@f_(1)(z) is ---

Let A = {0,1,2,3,} B={-3,-2,-1,0,1} and F: A rarr B the mapping defined by f(x) =x-3 , for all x in A . Show that f is one -one.

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 A={-1,1,2,-3}, B={2,8,18,32} and f: A rarr B be defined by, f(x)=2x^(2) , prove that, f is a many- one mapping of A into B