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.
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.
f : {1, 3, 4} → {1, 2, 5} is given by
f = {(1, 2), (3, 5), (4, 1)}
∴ f (1) = 2, f (3) = 5, f(4) = 1
Also g : {1, 2, 5} → {1, 3} is given by
g = {(1, 3), (2. 3), (5, 1)}
∴ g (1) = 3, g(2) = 3, g(5) = 1
Since co-domain of f is same as the domain of g
∴ g o f exists and (g o f) : {1,3,4 } → {1,3}
Now (g o f) (1) = g (f(1)) = g(2) = 3
(g o f)(3) = g (f(3)) = g(5) = 1
(g o f) (4) = g (f (4)) = g(1) = 3
∴ g o f = {(1, 3), (3, 1), (4, 3)}
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