SOLUTION: Find the domain of the function {{{f(x)=(1)/(3x+2)^2}}}

Question 140316: Find the domain of the function

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given function

Set the denominator equal to zero. Remember, dividing by 0 is undefined. So if we find values of x that make the denominator zero, then we must exclude them from the domain.

Take the square root of both sides

Subtract 2 from both sides

Combine like terms on the right side

Divide both sides by 3 to isolate x

Reduce

Since makes the denominator equal to zero, this means we must exclude from our domain

So our domain is:

which in plain English reads: x is the set of all real numbers except

So our domain looks like this in interval notation

note: remember, the parenthesis excludes -2/3 from the domain

If we wanted to graph the domain on a number line, we would get:

Graph of the domain in blue and the excluded value represented by open circle

Notice we have a continuous line until we get to the hole at (which is represented by the open circle).
This graphically represents our domain in which x can be any number except x cannot equal -2/3

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