Let f be the subset of `Z xx Z` defined by `f={(ab,a+b) : a,b in Z}`. Is f a function from Z to Z? Justify your answer.

Let f : R rarr R be defined by f(x) = cos (5x+2) . Is f invertible? Justify your answer.

Let R be the relation on Z defined by R= {(a,b): a, b in Z, a-b "is an integer"). Find the domain and range of R.

Let A={1,2,3,4}, B={1,5,9,11,15,16} and f={(1,5),(2,9),(3,1),(4,5),(2,11)} Are the following true? (i) f is a relation from A to B (ii) f is a function from A to B. Justify your answer in each case.

Which of the following functions from Z into Z are bijections ?

Let : f: N rarr N be defined by f(n)={{:((n+1)/2," if n is odd"),(n/2," if n is even"):} for all n inN . State whether the function f is bijective . Justify your answer.

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

Which of the following functions from Z to itself are bijections?

Let the function f ; R-{-b}->R-{1} be defined by f(x) =(x+a)/(x+b),a!=b, then