Question

Do I have this correct?:
Find the Domain of fog, f(x) x+1/x-2, g(x)=1/x

By composing I get:
1/x - 2

Then I set x to zero and get x ≠ 0

Therefore the Domain is x ≠ 0 ?

Answer 1

The domain of f is
\[ x \ne 2\]
since x = 2 gives you a 0 in the denominator. f(g(x)) would therefore imply that 1/x cannot be 2, therefore x cannot be 1/2.