can the domain be (-∞, ∞) if there is a verbal in the denominator?
To determine the domain of a function, you need to consider any potential restrictions or conditions on the input values. In the case of a fraction with a variable expression in the denominator, you need to ensure that the denominator does not equal zero, as division by zero is undefined.
If there is a variable expression in the denominator of the function, you need to find the values of that variable that would result in a zero denominator. So, to determine the domain, you solve the equation obtained by setting the denominator equal to zero.
If the equation has solutions, those solutions indicate where the function is not defined. Hence, these values must be excluded from the domain. However, if the equation has no solutions, the function is defined for all real numbers, and the domain is (-∞, ∞).
Take note that verbal terms can be converted to expressions for the purpose of finding the domain. If the verbal term includes variables that can take any real number, then the domain would be (-∞, ∞).
To summarize:
1. If the equation obtained by setting the denominator equal to zero has solutions, exclude those values from the domain.
2. If the equation has no solutions, the domain is (-∞, ∞).
Remember to always check the specific problem or function to determine if there are any additional conditions or restrictions on the domain.