Question

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

Accepted Answer

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}

Answer

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.

Answer

To determine the domain of the given function, we'll have to solve for x that makes the denominator zero.
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
It follows that the domain of the given function is the real set number, excepting the values {-2 ; 2}.
f(x): R-{-2 ; 2} -> R

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

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