In this rational expression, we need to find those values of x that can make the expression undefined. These values are those for which the denominator is equal to zero since a/0 is not defined. Then, we have:
[tex]x^2+7=0[/tex]
Now, we need to find the values of x for which this expression is equal to zero:
1. Subtract 7 from both sides of the equation:
[tex]x^2+7-7=0-7\Rightarrow x^2=-7\Rightarrow x=\pm\sqrt[]{-7}=x=\pm\sqrt[]{7i^2}[/tex]
We have values for complex roots. In this case, since we have this case, and the function must be in the set of the Real numbers, we can say that, in this function, we have no restrictions. In fact, if we graph the function, we have:
And we can see that the values for x are from -infinity to infinity (domain).
