## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Domain = $\mathbb{R}\backslash\{1\}$ or $\{x\in \mathbb{R}\ |\ x\neq 1\}$
The domain of a real function ( a function defined on real numbers) is the set of numbers for which f(x) is defined. $f(x)=\displaystyle \frac{x}{x^{2}-2x+1}\quad$ can be calculated for any real number, except for those yielding a zero in the denominator. Here, $x^{2}-2x+1=0\quad$ ... recognize a perfect square $(x-1)^{2}=0$ $x=1 \quad$must be excluded from the domain. Domain = $\mathbb{R}\backslash\{1\}$ or $\{x\in \mathbb{R}\ |\ x\neq 1\}$