Originally Posted by

**hooke** Say i am given 2 functions , f(x) and g(x) with their respective domains , is it possible for me to know the domain of f o g without evaluating function f o g ?

Example :

$\displaystyle f(x)=\sqrt{x-1}$ , $\displaystyle x\geq 1$

$\displaystyle g(x)=\frac{1}{x-1}$ , $\displaystyle x\in R$ , $\displaystyle x\neq 1$

$\displaystyle fg(x)=\sqrt{\frac{1}{x-1}-1}$

i see that the expression under the square roots must be >=0 , so

$\displaystyle 1\leq x \leq 2$ but since $\displaystyle x\neq 1$ so the domain is $\displaystyle 1<x\leq 2$

Thats how i would do it . Is there an easier way ?