Its the same thing.

take k(x) for example.

h(x) = x or we say the function h(x), graphed as y = x

hence h(k(x)) = k(x)

Given k(x) = x + 2
we know hk(x) = (x + 2)

formalising an idea,
for an unknown function z(x),
if k(x) is a known function.

and zk(x) can be expressed as y = a + b(k(x)) + c or a function of k(x), for a,c, are known constants/parameters.
then z(x) is simply y = a + bx + c

which is how TS, used the "completing the Square method, to obtain the equation as a factor of (k(x))
and work out h(x). An alternative method from inversing the identity.

what method wrong?