Solution:
(a) Given the functions:

Then:

Similarly,

Two functions f and g are inverses of each other if and only if f(g(x))=x for every value of x in the domain of g and g(f(x))=x for every value of x in the domain of f.
ANSWER: f and g are inverse of each other.
(b) Given:

Then:

Also,

ANSWER: f and g are not inverses of each other.