Let f be a real function given by . Find each of the following:
fof
We have, f(x) =
Clearly, domain of f = [2, ∞] and range of f = [0, ∞)
We observe that range of f is not a subset of domain of f
∴ Domain of (fof) = {x: x ϵ Domain of f and f(x) ϵ Domain of f}
= {x: x ϵ [2, ∞) and ϵ [2, ∞)}
= {x: x ϵ [2, ∞) and ≥ 2}
= {x: x ϵ [2, ∞) and x – 2 ≥ 4}
= {x: x ϵ [2, ∞) and x ≥ 6}
= [6, ∞)
Now,
fof(x) = f(f(x)) = f =