Let f(x)=1/x and g(x)= x^2-2x. What two numbers are not in the domain of fog?

Question

ganeshie8 · Answer

Clearly g(x) = x^2-2x has no restrictions, 
so simply find the restrictions of f(g(x)) = f(x^2-2x) = 1/(x^2-2x)

ganeshie8 · Answer

$$f(g(x))=\dfrac{1}{x^2-2x}$$

what values of $x$ make that expression go crazy  ?

anonymous · Answer

Well, is 0 one of them? @ganeshie8

ganeshie8 · Answer

Yes, simply set the bottom equal to 0 and solve x :
$$x^2-2x=0$$

anonymous · Answer

@ganeshie8 x= -2? so it would be 0,-4?

anonymous · Answer

-2*

ganeshie8 · Answer

$x^2-2x=0 $

$x(x-2)=0$

$x=0$ or $x-2=0$

that gives you $x~=~0, ~~2$

ganeshie8 · Answer

$0, 2$ are the two numbers that must be excluded from the domain of fog

astrophysics · Answer

Usually when I set it up for the domain I write it as $$x^2-2x \neq 0$$ then solve for x, then you know you are looking for the restrictions. That's just a quick tip for rational functions :P