Question

Find the domain of the rational function.

$G\left(x\right)=\frac{x-3}{x^2+1}$

Short answer

The domain of the function is all real numbers. i.e.,$\left(-\infty ,\infty \right)$

Step-by-step solution

Step 1. Given information  

The given function is $G\left(x\right)=\frac{x-3}{x^4+1}$

Step 2. Find the domain

For the domain, the denominator should not be equal to zero.

so,

$$\begin{gathered} x^4+1\ne 0 \\ {x}^4\ne -1 \end{gathered}$$

There is no solution of this equation.

So, The domain of the function is all real numbers. i.e.,$\left(-\infty ,\infty \right)$