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Combination of Functions

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My answer: {x e R | x ≤ -11} Is that correct?

Jan 14, 2018

#1
+16477
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The first one has a domain of

-14   -13   -12   -11   -10  -9 ......etc

The SECOND one has a domain of

-11  -12  -13  -14  -15  -16.....

The common numbers (in color) define the new domain after adding the functions....the minimum is   -14   that will satisfy both of the domain restrictions given....

Jan 14, 2018
edited by ElectricPavlov  Jan 14, 2018
edited by ElectricPavlov  Jan 14, 2018
#2
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So x ≤ -14 and x e R ?

Julius  Jan 14, 2018
#3
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The question asks what is the minumum value in the domain of  (g+f)(x) :      -14

The domain   is   -14  -13   -12  -11         Cool?

ElectricPavlov  Jan 14, 2018
#4
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Whatever  x  value we choose to plug in to  (g + f)(x)  has to be in the domain of both  g(x)  and  f(x) .

For instance, we can't find  g(1) + f(1)  because we can't find  g(1) .

The domain of  g + f  is all real  x  values such that   x ≥ -14  and  x ≤ -11

The domain of  g + f  is all real  x  values such that   -14 ≤ x ≤ -11

The minimum value in that domain is  -14  .

Jan 15, 2018
#5
+956
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Ohh I see, they're asking for a value.

Thanks everyone!

Jan 15, 2018