Q9 of 70 Page 11

If the mappings f and g are given by f = {(1, 2), (3, 5), (4, 1)} and g = {(2, 3), (5, 1), (1, 3)}, write f o g.

We have,

f = {(1, 2), (3, 5), (4, 1)} and g = {(2, 3), (5, 1), (1, 3)}

Domain of g = {2,5,1}

Now, fog(2) = f(g(2)) = f(3) = 5

fog(5) = f(g(5)) = f(1) = 2

fog(1) = f(g(1)) = f(3) = 5

∴ fog = {(2, 5), (5, 2), (1,5) }

Is g = {(1, 1), (2, 3), (3, 5), (4, 7)} a function? If g is described by g (x) = α x + β, then what value should be assigned to α and β.

Are the following set of ordered pairs functions? If so, examine whether the mapping is injective or surjective.

(i) {(x, y): x is a person, y is the mother of x}.

(ii){(a, b): a is a person, b is an ancestor of a}.

Let C be the set of complex numbers. Prove that the mapping f :C → R given by f (z) = |z|, ∀ z ∈ C, is neither one-one nor onto.

Let the function f :R → R be defined by f (x) = cosx, ∀ x ∈ R. Show that f is neither one-one nor onto.