find the domain of f(x)=5/¡Ì(x2-4)
To find the domain of a given function, you need to identify all the values of x for which the function is defined. In this case, f(x) = 5/√(x^2 - 4).
To determine the domain:
1. Start by considering the expression inside the square root, x^2 - 4, and solve for the values of x that make it zero.
x^2 - 4 = 0
(x - 2)(x + 2) = 0
2. Next, find the values of x that satisfy the equation (x - 2)(x + 2) = 0. In this case, x can either be -2 or 2 because those values will make the denominator of the fraction equal to zero.
3. However, the function is not defined when the denominator is zero because dividing by zero is undefined. Therefore, x = -2 and x = 2 must be excluded from the domain.
Hence, the domain of the function f(x) = 5/√(x^2 - 4) is all real numbers except x = -2 and x = 2.
In interval notation, this can be written as (-∞, -2) ∪ (-2, 2) ∪ (2, ∞).