How do you find the domain of this function #f(x)=1/(3x-6)#?

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2 Answers
Alan P.
Apr 25, 2015

The only value of #x# for which #f(x) = 1/(3x-6)# is not defined is #x=2# (since this would result in division by zero).

The Domain of #f(x)# is
#(-oo,2)uu(2,+oo)#

bp
Apr 25, 2015

Domain #(-oo,2)U(2,oo)#

To find the domain of a function, we first identify the values of x for which f(x) becomes undefined. In the present case, it is observed that if x=2, then f(x) becomes #1/0# or #oo#. Hence the domain would be all real numbers except 2. In interval notation it can be expressed as #(-oo,2)U(2,oo)#. In the set builder notation it would be written as {x:#inR# | x#!in#2}

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