Give examples of two surjective function `f_1` and `f_2` from `Z` to `Z` such that `f_1+f_2` is not surjective.

Give examples of two one-one functions f_1 and f_2 from R to R such that f_1+f_2: R->R , defined by (f_1+f_2)(x)=f_1(x)+f_2(x) is not one-one.

Give examples of two functions f: N->Z" and "g: Z->Z such that gof is injective but g is not injective. (Hint: Consider f(x) = x" and "g(x) = |x| )

Give examples of two functions f:" "N->Z" "a n dg:" "Z->Z such that o f is injective but is not injective. (Hint: Consider f(x)" "=" "x" "a n d""""""""g(x)" "=" "|x| )

Statement 1 : For a continuous surjective function f: RvecR ,f(x) can never be a periodic function. Statement 2: For a surjective function f: RvecR ,f(x) to be periodic, it should necessarily be a discontinuous function.

Let R be the set of real numbers. If f:R->R is a function defined by f(x)=x^2, then f is injective but not surjective surjective but not injective bijective none of these (a) injective but not surjective (b) surjective but not injective (c) bijective (d) non of these

Let f: A to B; g: B to A be two functions such that gof = I_A . Then; f is an injection and g is a surjection.

Let f:N to Z and f (x)=[{:((x-1)/(2),"when x is odd"),(-(x)/(2),"when x is even"):}, then: (a). f (x) is bijective (b).f (x) is injective but not surjective (c).f (x) is not injective but surjective (d).f (x) is neither injective nor subjective

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

Let f: A to B; g: B to A be two functions such that fog = I_B . Then; f is a surjection and g is an injection.

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