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.
f : Z → Z, is defined by f = {(n, n2) : n ∈ Z}
∴ Df = Z and f (n) = n2 Again g : Z → Z is defined by g = {(n, | n |2 ) : n ∈ Z}
∴ Dg = Z and g (n) = | n |2 = n2 = f (n)
∴ Df = Dg and f (n) = g (n) ∀ n ∈ Df or Dg
∴ 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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