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## Homework Statement

The sets A and B are defined respectively by

[tex]A={x\in R : 0\leq x\leq 1}[/tex]

[tex]B={x\in R : 1\leq x\leq 2}[/tex]

and the functions f and g are defined respectively by

[tex]f(x)=x^2-2x+2[/tex]

[tex]g(x)=\frac{x+2}{x-1}[/tex]

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

## Homework Equations

## The Attempt at a Solution

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

so the range is (1, infinity)