g(x) = (x^3 - x)/(x - 1) lim g(x) x->1

Explanation:

Step1: Factor the numerator

$x^{3}-x=x(x^{2} - 1)=x(x + 1)(x - 1)$

Step2: Simplify the function

$g(x)=\frac{x(x + 1)(x - 1)}{x - 1}=x(x + 1)$ for $x\neq1$

Step3: Calculate the limit

$\lim_{x\rightarrow1}g(x)=\lim_{x\rightarrow1}x(x + 1)$ Substitute $x = 1$ into $x(x + 1)$: $1\times(1 + 1)=2$

Answer:

$2$