Short Answer TypeCheck 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
In each of the following cases, state whether the function is one-one, onto or bijective. Justify your answer.
f : R → R defined by f(x) = 3 – 4x
f : R → R defined by f(x) = 3 – 4x
Let, 
such that f(x1) = f(x2)
3 - 4x1 = 3 - 4x2
f is one-one
For any real number (y) in R, there exists 
in R such that 
f is onto
Hence, f is bijective.
In each of the following cases, state whether the function is one-one, onto or bijective. Justify your answer.
f : R → R defined by f(x) = 1 + x2
Consider the binary operation A on the set {1, 2, 3, 4, 5} defined by a ∧ b = min. {a, b}. Write the operation table of the operation ∧.
Let A = Q x Q. Let be a binary operation on A defined by (a, b) * (c, d) = (ac, ad + b).
Then
(i) Find the identify element of (A, *)
(ii) Find the invertible elements of (A, *)
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