Determine the domain of the function f(x) = 1/(x-2) .

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The domain of a function f(x) is all values of x for which f(x) gives a real value. Here we have f(x) = 1/(x - 2). We see that f(x) gives a real value for all values of x except when x = 2. In that case 1/(x - 2) = 1/0 = indeterminate.

**The domain of f(x) is R - {2}**

The domain of a function is the set of x values that makes the function to exist.

In this case, the expression of the function is a ratio. A ratio is defined if and only if it's denominator is different from zero.

We'll write mathematically the constraint of existence of the function:

x - 2 different from 0.

We'll add 2 and we'll get:

x different from 2.

**The domain of the given function is: (-infinite ; 2) U (2 ; +infinite).**

**We can also write the domain of the function as: R - {2}.**

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