Question

For what value or values of x, if any, are the following functions not defined?f(x)= 1/ √(1-x) (x-2)

Answer 1

you have to make sure that the thing inside the radical is positive

Answer 2

so you have to solve
\[(1-x)(x-2)>0\]
the zeros of
\[(1-x)(x-2)\] are 1 and 2, and this is a parabola that faces down. so it will be negative outside the zeros and positive between them

Answer 3

you solution therefore is
\[1<x<2\] or as an interval
\[(1,2)\]