Question

F(x)= 1/x+2and g(x)=2/x−4,find the domain of f(g(x))

Answer 1

`(-\infty,3)\cup(3,\infty)`

Explanation:

`\displaystyle f(g(x))=f\biggr((2)/(x-4)\biggr)=(1)/((2)/(x-4)+2)`

`\displaystyle (2)/(x-4)+2\\eq0\\\\(2)/(x-4)\\eq-2\\\\2\\eq-2x+8\\\\-6\\eq-2x\\\\x\\eq3`

Therefore, since
`x\\eq 3` as it makes the denominator 0, then the domain of the composite function
`f(g(x))` is
`(-\infty,3)\cup(3,\infty)`.