Check the injectivity and surjectivity of the following function f : N → N given by f(x) = x square

Check the injectivity and surjectivity of the following functions: (i) f : N ->N given by f(x)=x^2 (ii) f : Z-> Z given by f(x)=x^2 (iii) f : R ->R given by f(x)=x^2 (iv) f : N-> N given by f(x)=x^3 (v) f : Z → Z given by f(x) = x^3

Discuss the surjectivity of the following functions: f: R-> given by f(x)=x^3+2 for all x in Rdot

Check the nature of the following function. (i) f(x)=sin x, x in R " (ii) " f(x) =sin x, x in N

Check the continuity of the function f given by f(x) = 2x + 3 a t x = 1 .

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

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

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

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

Discuss the surjectivity of f: Z->Z given by f(x)=3x+2 for all x in Z .

If f(x) is a real valued function, then which of the following is injective function ? (i) f(x) = x^(5) (ii) f(x) = x + sin x (iii) f(x) = x^(2) (iv) f(x) = e^(x) (v) f(x) = x^(3) + x^(2) + 4x + 4