Mathematics

Problem

Let

f:[1,\infty)\to[0,\infty)

be defined by

f(x)=\sqrt{x-1}

and let

g: \mathbb R \to \mathbb R

be defined by

g(x)=x-2

. Define

h(x)=(f^{-1}\circ g)(x)

. Determine the set of all real numbers

x

for which

h(x)

is defined.