There's one more value of ##x## which must be excluded.cavalieregi said:
After excluding ##1-x^2 = 0##, you are left with either ##1 - x^2 < 0## or ##1 - x^2 > 0##. Try writing these inequalities in terms of ##x## instead of ##x^2##.
A rational function is a mathematical function that can be expressed as the ratio of two polynomial functions. It can be written in the form f(x) = p(x)/q(x), where p(x) and q(x) are both polynomial functions and q(x) is not equal to 0.
The domain of a rational function is the set of all possible input values for which the function is defined. In other words, it is the set of all real numbers x for which the denominator of the rational function is not equal to 0.
To find the domain of a rational function, you need to determine the values of x that make the denominator of the function equal to 0. These values are not included in the domain. The remaining values of x will make up the domain of the rational function.
Yes, there are some restrictions on the domain of a rational function. As mentioned earlier, the denominator of a rational function cannot be equal to 0. In addition, some rational functions may have other restrictions on the domain due to the presence of square roots or even/odd powers of x. It is important to check for these restrictions when finding the domain of a rational function.
Yes, it is possible for the domain of a rational function to be an empty set. This can happen when the denominator of the rational function is always equal to 0, meaning that there are no possible values of x that will make the function defined. In this case, the rational function has no domain and is considered undefined.