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.

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.

Show that the function f: R to R given by f (x) = x ^(3) is injective.

Let S be the set of all triangles and R^+ be the set of positive real numbers. Then the function f: SrarrR^+,f(Delta)=area of Delta ,where Delta in S , is injective but not surjective. surjective but not injective injective as well as surjective neither injective nor surjective

Let f: R->R and g: R->R be two given functions such that f is injective and g is surjective. Then which of the following is injective? (a) gof (b) fog (c) gog (d) none of these

Let R be the set of real numbers. If f:R->R is a function defined by f(x)=x^2, then f is (a) injective but not surjective (b) surjective but not injective (c) bijective (d) non of these

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

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 :

If z_1, z_2, z_3 be the affixes of the vertices A, B and C of a triangle having centroid at G such that z = 0 is the mid point of AG then 4z_1 + z_2 + z_3 =

f + g may be continuous function, if

Let f:[-oo,0)->(1,oo) be defined as f(x)=(1+sqrt(-x))-(sqrt(-x)-x) then f(x) is (A) injective but not surjective (B) injective as well as surjective (C) neither injective nor surjective (D) surjective nut not injective