(a) Since
and
, we have

We're given that

but we can rewrite this as

(bear in mind that we can only do this so long as x ≠ 0) so it follows that

(b) On its own, we may be tempted to conclude that the domain of
is simply x ≠ -1. But we should be more careful. The domain of a composite depends on each of the component functions involved.
is defined for all x - no issue here.
is defined for all x ≠ 0. Then
also has a domain of x ≠ 0.
is defined for all x ≠ -1, but

is undefined not only at x = -1, but also at x = 0. So the domain of
is
