MHB Stephanie's question at Yahoo Answers (Domain question)

[Fernando Revilla]

Here is the question:

f(x) = (1) / (4 / ((x-1) - 2))

I got the 3 but I can not get the 1.

Can you possibly tell me what this would be called so I can google it, and if possible explain mathematically how to get the 1; besides substituting in numbers?

Here is a link to the question:

Math Help - Domain Question? - Yahoo! Answers

I have posted a link there to this topic, so the OP can find my response.

 

[Fernando Revilla]

Re: Stepanie's question at Yahoo! Answers (Domain question)

Hello Stephanie,

The funcion is $f(x)=\dfrac{1}{\dfrac{4}{x-1}-2}$. But $\dfrac{4}{x-1}$ is defined if and only if $x\neq 1$ so, $$f(x)=\dfrac{1}{\dfrac{4-2x+2}{x-1}}=\dfrac{x-1}{6-2x}\quad (\mbox{if }x\neq 1)$$ For $x\neq 1$, $f(x)$ is defined if and only if $x\neq 3$. Hence, $\mbox{Dom } f=\mathbb{R}-\{1,3\}$