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

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Given the function f(x) = 1/(x-2).

We need to find the domain of f(x).

We know that the domain are all x values such that the function is defined.

Then, we will find the values in which f(x) is not defined.

Since f(x) is a fraction, then the denominator can not be zero.

==> x -2 = 0

==> x = 2

Then the function is not defined when x = 2.

Then the domain of f(x) is all real numbers except for 2.

**==> The domain = 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}.**

f(x) = 1/(x-2).

The domain of the function f(x) = 1/(x-2) is the set of values of x for which the f(x) real and exists.

1/(x-2) is defined for all x but not for x = 2 when the denominator in 1.(x-2) becomes zero. So f(x) is not defined for x= 0.

So x can take any real value but not x = 2, as f(x) is defined for all values other than zero.

So the domain of x is (-infinity, +infinity} - {2}.