Give examples of two functions `f : N to N and g : N to N` such g o f is onto but f is not onto.

Give examples of two functions f:N to Z and g: Z to Z such that g o f is injective but g is not injective.

Show that the function f: N to N, given by f (x) =2x, is one-one but not onto.

Show that if f:A to B and g: B to C are onto, then gof :A to C is also onto.

Let N be the set of natural numbers and two functions f and g be defined as f, g : N to N such that : f(n)={((n+1)/(2),"if n is odd"),((n)/(2),"if n is even"):}and g(n)=n-(-1)^(n) . The fog is :

Are f and g both necessarily onto, if gof is onto ?

Show that the function f:N to N, given by f (1) =f (2) =1 and f (x) =x -1, for every x gt 2, is onto but not one-one.

Let A be the set of all 50 students of Class X in a school Let f: A to N be function defined by f(x) = roll number of the student x. Show that f in one-one but not onto.

If f and g are two functions defined on N , such that f(n)= {{:(2n-1if n is even), (2n+2 if n is odd):} and g(n)=f(n)+f(n+1) Then range of g is (A) {m in N : m= multiple of 4 } (B) { set of even natural numbers } (C) {m in N : m=4k+3,k is a natural number (D) {m in N : m= multiple of 3 or multiple of 4 }

If f and g are one-one functions, then (a) f+g is one one (b) fg is one one (c) fog is one one (d) n on e of these

Let f: R->R be any function. Also g: R->R is defined by g(x)=|f(x)| for all xdot Then g is a. Onto if f is onto b. One-one if f is one-one c. Continuous if f is continuous d. None of these