# What is the domain of 4x^2-x-3 ?

The domain of $4 {x}^{2} - x - 3$ is the whole of $\mathbb{R}$, that is $\left(- \infty , \infty\right)$.
Any polynomial in $x$ is well defined for any real value of $x$.
The domain could actually be any set of numbers (or certain other algebraic objects), but conventionally it is often assumed that the intended domain is the maximal subset of $\mathbb{R}$ for which the function is defined.
So conventionally, the domain of $4 {x}^{2} - x - 3$ is the whole of $\mathbb{R}$.