Pretty good.
gf(1) cannot be formed, using your notation for function composition, because f(1) is not in the domain of g, not because 1 is not in g's domain.
g(f(1)) would be better notation
The functions f and g have domains (0,inf) and (2,inf) respectively and are defined by
f(x) =
g(x) =
a] write down the ranges of f and g.
range of f = (-1 , inf)
range of g = (3, inf)
b] give the reason why gf(1) cannot be formed.
Because 1 is not in the domain of g.
c] find a simplified expression for fg(x)
=
d] state the domain and range of fg.
domain = (2, inf)
range = (8, inf)
Do you believe that my answers correct? These were from an exam and I am hoping that they were correct. Thanks
PS - take inf to mean infinity!