g(x) = (-2x² + x)/x\nlim x→0 g(x)

Explanation:

Step1: Simplify the function

First, simplify $g(x)=\frac{-2x^{2}+x}{x}$. Factor out $x$ from the numerator: $g(x)=\frac{x(-2x + 1)}{x}$. For $x\neq0$, we can cancel out the $x$ terms, so $g(x)=-2x + 1$.

Step2: Find the limit

Now, find $\lim_{x\rightarrow0}g(x)$. Substitute $x = 0$ into the simplified - function $y=-2x + 1$. Using the limit rule $\lim_{x\rightarrow a}(mx + b)=ma + b$ (where $m=-2$, $b = 1$, and $a = 0$), we have $\lim_{x\rightarrow0}(-2x + 1)=-2\times0+1$.

Answer:

$1$