Find the domain of the function.  f(x)=1/(3x-12)

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flbyrne's profile pic

flbyrne | (Level 3) Assistant Educator

Posted on

Find the domain of the function:

`f(x)=1/(3x-12)`

The function is undefined for x values such as:

`3x-12=0`

`3x=12`

`x=12/3=4`

Thus the domain of the function is (-`oo`,4) and (4,`oo`)

kingattaskus12's profile pic

kingattaskus12 | (Level 3) Adjunct Educator

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Since the given function is a rational function,the domain is the set of all real numbers except for the value of x that will make the denominator equal to zero. This gives us

In other words, the domain is the set of all real numbers except 4. When written in interval notation, the domain will be

`(-oo,4)uu(4,oo)`

tonys538's profile pic

tonys538 | Student, Undergraduate | (Level 1) Valedictorian

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The domain of a function y = f(x) is the set of values in which x lies for which the value of y is real and defined.

For the function f(x)=1/(3x-12) consider the denominator 3x - 12, the fraction 1/(3x - 12) is not defined when 3x - 12 = 0

3x - 12 = 0 when 3x = 12 or x = 4

The required domain is the set of real numbers other than 4 or R - {4}

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