Question

What is the domain of the function f(x) = (1 - e^x²)/(1 - e¹ - x² )?

a) All real numbers
b) x ∈ ℝ | x ≠ ± 1
c) x ∈ ℝ | x ≠ 0
d) x ∈ ℝ | x ≠ 1

Answer 1

The domain of the function f(x) = (1 - e^x²)/(1 - e¹ - x²) includes all real numbers, as the denominator never equals zero.

Step-by-step explanation:

The domain of a function refers to the set of all possible input values (x-values) for which the function is defined. Looking at the given function f(x) = (1 - e^x²)/(1 - e¹ - x²), we need to identify the values of x for which the denominator is not equal to zero, since division by zero is undefined. The denominator is 1 - e¹ - x², which is equivalent to 1 - e - x². Setting the denominator equal to zero gives us x² = 1 - e, but since e (Euler's number) is approximately 2.718, the expression 1 - e is negative, which means there's no real number x that can make the expression equal to zero. Therefore, the domain of the function f(x) includes all real numbers, and the correct answer is a) All real numbers.