The sets A and B are defined respectively by

$\displaystyle A={x\in R : 0\leq x\leq 1}$

$\displaystyle B={x\in R : 1\leq x\leq 2}$

and the functions f and g are defined respectively by

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

$\displaystyle g(x)=\frac{x+2}{x-1}$

where f(A)=B , g(B)=C with C as the range of the function g .

Find the range of the composite function gf(A)=C

Attempt :

The way they put it kinda confuse me .

$\displaystyle gf(x)=1+\frac{3}{(x-1)^2}$ , with domain [0,1)

so the range is (1, infinity)