Mark the correct alternative in each of the following:

Let f : R → R be a function defined by Then,

A. f is a bijection

B. f is an injection only

C. f is surjection on only

D. f is neither an injection nor a surjection

Let f :R → R be given by f (x) = tan x. Then f^–1 (1) is

| Let * be a binary operation on Q defined by

Show that * is commutative as well as associative. Also find its identity elements, if it exists.

Find the identity element in the set Q + of all positive rational numbers for the operation * defined by for all a, b ∈ Q +.

Let f : A → B and g : B → C be the bijective functions. Then (g o f)^–1 is

Show that the binary operation * on defined as for all is commutative and associative on A. Also find the identify element of * in A and prove that every element of A is invertible.

Determine whether each of the following operations define a binary operation on the given set or not:

‘*’ on Q defined by for all a,b Q.