Let f : x → Y be an invertible function. Show that the inverse of f^–1 is f,

i.e.(f^–1)^–1 = f.

Let f : N → Y be function defined as f (x) = 4 x + 3, where, Y = {y ∈N : y = 4 x + 3 for some x ∈ N}. Show that f is invertible. Find the inverse.

Let R be the relation in the set N given by R = {(a, b) : a = b – 2, b > 6}. Choose the correct answer. (A) (2, 4) ∈ R    (B) (3, 8) ∈ R     (C) (6, 8) ∈ R    (D) (8, 7) ∈ R

Show that the function f : R_. → R_. defined by  is one-one and onto, where R_. is the set of all non-zero real numbers. Is the result true, if the domain R_. is replaced by N with co-domain being same as R_.?

Check the injectivity and surjectivity of the following functions:
f : N → N given by f(x) = x² 

Check the injectivity and surjectivity of the following functions:
f : Z → Z given by f(x) = x²