Short Answer TypeFind the number of all one-one functions from set A = {1, 2, 3} to itself.
A = {1, 2, 3}
Let f = A → A be a one-to-one function. Then f (1) has three choices, namely 1, 2 or 3. So f (1) = 1 or f (1) = 2 or f (1) = 3.
Similarly f (2) and f (3) have three choices each.
all the one-to-one functions from A to A are
(i) {(1, 1), (2, 2), (3, 3)} (ii) (1, 1), (2, 3), (3, 2)}
(iii) {(1.2). (2, 3), (3, 1)} (iv) {(1, 2), (2, 1), (3, 3)}
(v) {(1,3), (2, 2), (3, 1)} (vi) {(1, 3), (2, 1), (3, 2)}
required number of functions = 6
Let f : Z → Z, g : Z → Z be functions defined by
f = {(n, n2): n ∈ Z} and g = {(n | n |2): n ∈ Z}. Show that f = g.
Let f : R → R be defined as f (x) = x4 Choose the correct answer.
(A) f is one-one onto (B) f is many-one onto
(C) f is one-one but not onto (D)f is neither one-one nor onto.
Let f : R → R be defined as f (x) = 3 x. Choose the correct answer. (A) f is one-one onto (B) f is many-one onto
(C) f is one-one but not onto (D) f is neither onc-one nor onto.
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