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

f(x) = $\displaystyle x^2 - 1$

g(x) = $\displaystyle 2x - 1$

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)

= $\displaystyle 4x^2 - 4x$

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!