# Math Help - Domain and range of composed functions

1. ## Domain and range of composed functions

The functions f and g have domains (0,inf) and (2,inf) respectively and are defined by

f(x) = $x^2 - 1$
g(x) = $2x - 1$

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)

= $4x^2 - 4x$

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!

2. 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