Which is the domain of the function f(x)=x/(3x-1)?

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on


First we need to determine x values where f(x) is not defined. Since f is a ratio, then the function is not defined when 3x-1=0


==> x= 1/3

then the domain is R-{1/3}

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll establish the domain knowing the fact that the division by 0 is not allowed.

For this reason, we'll find out first, the x values for the denominator is cancelling.

3x-1 = 0



From here we conclude that the function is not defined for x=1/3

So, the domain of definition is:

R (the real set of numbers)-{1/3}

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

To find the domain of x/(3x-1).

f(3x-1) bbecomes undefined and discontnous at 3x-1 = 0. )r

at 3x= 1. )r

x = 1/3.

So , (-infinity < x <1/3) U (1/3 < c < infinity) is the domain of x. or x can take all real values except x= 1/3

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