Short Answer TypeLet 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.
f : R → R is given by f (x) = x4
Different elements in R can have the same image
[∵ f (–2) = (–2)4 = 16, f (2) = (2)4 = 16]
∴ f is not one-one.
Also Rf = set of non-negative reals ≠ R ∴ f is not onto.
∴ f is neither one-one nor onto.
∴ (D) is correct answer.
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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