Question

If the inverses of two functions are both functions, will the inverse of the composite function made by the original functions also be a function?

Answer 1

Let the two functions be f(x) and g(x).
Create the sum or composite of the functions as
h(x) = f(x) + g(x).

In order to have inverses, both f(x) and g(x) should pass the vertical line test
Therefore the sum (or difference) of the two functions, h(x), will also pass the vertical line test.

Answer:
Because h(x) passes the vertical line test, it follows that the inverse of the composite function made by the original functions is also a function.