I need a little help here-not sure if I got it right:
f(x)= 2/x+1, g(x)= x/x+1
domain of f is {x is part of a set where x >0} and domain of g is {x is part of a set where x is greater than or equal to 0} [0, infinity)U(0,infinity).
OK
Both of the functions are rational functions... in other words, of the form
$\displaystyle f(x) = \frac{g(x)}{h(x)}$, where $\displaystyle g(x)$ and $\displaystyle h(x)$ are continuous functions of $\displaystyle x$.
$\displaystyle f(x)$ is also continuous at all points except where the denominator $\displaystyle (h(x))=0$.
So where does the denominator equal 0? In both cases, where $\displaystyle x = -1$.
So the domain of each function is $\displaystyle \mathbf{R}\backslash \{-1\}$.
Sorry for the double post, didn't realise I edited the first one instead of adding a new one.
OK
Both of the functions are rational functions... in other words, of the form
, where and are continuous functions of .
is also continuous at all points except where the denominator .
So where does the denominator equal 0? In both cases, where .
So the domain of each function is $\displaystyle \mathbf{R} \backslash \{-1\}$.