Question

What is the domain of the function f(x) = 2/x²-3 ?

A) All real numbers
B) x ∈ ℝ, x ≠ 0, √3, and x ≠ - √3
C) x ∈ ℝ, x ≠ 3 and x ≠ - √3
D) x ∈ ℝ, x ≠ 0, x ≠ √3, and x ≠ - √3

Answer 1

The domain of the function f(x) = 2/(x²-3) is all real numbers except x = √3 and x = -√3, as these values make the denominator zero and the function undefined.

Step-by-step explanation:

To find the domain of the function f(x) = 2/(x²-3), we need to identify all values of x for which the function is defined. A function with a variable in the denominator, like this one, is undefined whenever the denominator is equal to zero. Therefore, we set the denominator equal to zero and solve for x:

x² - 3 = 0

By adding 3 to both sides, we get:

x² = 3

Taking the square root of both sides, we find:

x = ±√3

Therefore, the function is undefined at x = √3 and x = -√3. The domain of the function includes all real numbers except √3 and -√3. Hence, the correct answer is:

B) x ∈ ℝ, x ≠ √3, and x ≠ - √3