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What is the domain of the function

$$f(x) = \frac{(2x-3)(2x+5)}{(3x-9)(3x+6)}~?$$

Express your answer as an interval or as a union of intervals.

 Feb 15, 2021
edited by powclaire  Feb 15, 2021
 #1
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(−∞,−2)∪(−2,3)∪(3,∞)

 Feb 15, 2021
 #2
avatar+120129 
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We  cannot  have     (3x  -9)  = 0   or  ( 3x + 6)  = 0

 

So

 

3x  - 9    =  0                               3x + 6  = 0

3x  = 9                                         3x   =  -6

x  =9/3   = 3                                  x =  -6 / 3    = -2

 

 

So....the  two   values of x NOT in the  domain  are    x =  -2    and  x   =3

 

The domain is

 

(-infinity , -2 )  U  ( 3  , infinity )

 

See  the graph here  :   https://www.desmos.com/calculator/rv5xizgbtu

 

 

cool cool cool

 Feb 15, 2021

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