Question

Let f and g be two real functions given by f = {(10, 1), (2, 0), (3, −4), (4, 2), (5, 1)} and g = {(1, 0), (2, 2), (3, −1), (4, 4), (5, 3)}. Then the domain fg is given by __________ .

Answer 1

f = {(10, 1),(2, 0), (3, –4), (4, 2), (5, 1)}
g = {(1, 0), (2, 2), (3, –1), (4, 4), (5, 3)}

Since (fg) (x) = f(x) g(x)
∴ Domain of fg is (Domain of f) ∩ (Domain of g)
Since Domain of f = {10, 2, 3, 4, 5}
Domain of g = {1, 2, 3, 4, 5}
⇒ Domain of f g is {2, 3, 4, 5}