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How to find domain of function f(x)=(x-2)/(x^2-4)? How to find domain of function f(x)=(x-2)/(x^2-4)?

| Certified Educator

The domain of a function f(x) is all the values x for which f(x) gives real values.

f(x)=(x-2)/(x^2-4)

=> (x - 2)/(x - 2)(x + 2)

=> 1/(x + 2)

This is not defined when x = -2

The domain is R - {-2}

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giorgiana1976 | Student

The domain of a function contains all x values that makes the function to exist.

To determine the domain of the given function, we'll have find first the x values that cancel denominator, to exclude them from domain.

x^2 - 4 = 0

We notice that the denominator is a difference of squares:

(x - 2)(x + 2) = 0

We'll put each factor as zero:

x - 2 = 0

x = 2

x + 2 = 0

x = -2

The domain of the function is the real set number, excepting the values {-2 ; 2}; f(x): R-{-2 ; 2} -> R.