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...
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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}.
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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