Question

Answer the following:

Let f : R – {2} → R be defined by f(x) = `(x^2 - 4)/(x - 2)` and g : R → R be defined by g(x) = x + 2. Examine whether f = g or not

Answer 1

Since 2 ∉ domain of f, f(2) does not exist whereas g(2) exist because 2 ∈ domain of g and g(2) = 2 + 2 = 4

∴ f(x) ≠ g(x) for all x

Hence, f ≠ g.