SOLUTION: Find the domain of f(t)=(t+3)/(t(t+2)) Thank You

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Question 146268: Find the domain of f(t)=(t+3)/(t(t+2))
Thank You
Found 2 solutions by scott8148, jim_thompson5910:
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
the domain consists of all values which result in a value for the function

if t equals 0 or -2, division by zero results __ this is a no-no (UNDEFINED)

so the domain is all real numbers EXCEPT 0,-2

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
f%28t%29=%28t%2B3%29%2F%28t%28t%2B2%29%29 Start with the given function


t%28t%2B2%29=0 Set the denominator equal to zero. Remember, dividing by 0 is undefined. So if we find values of t that make the denominator zero, then we must exclude them from the domain.


Set each factor equal to zero:

t=0 or t%2B2=0

t=0 or t=-2 Now solve for t in each case


So our solutions are t=0 or t=-2



Since t=-2 and t=0 make the denominator equal to zero, this means we must exclude t=-2 and t=0 from our domain

So our domain is:

which in plain English reads: t is the set of all real numbers except t%3C%3E-2 or t%3C%3E0

So our domain looks like this in interval notation


note: remember, the parenthesis excludes -2 and 0 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 values represented by open circles

Notice we have a continuous line until we get to the holes at t=-2 and t=0 (which is represented by the open circles).
This graphically represents our domain in which t can be any number except t cannot equal -2 or 0