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Suppose a function f(x)  is defined on the domain [-8,4]. If we define a new function g(x) by

g(x) = f(2x - 1)

then what is the domain of g(x)? Express your answer in interval notation.

 May 9, 2021
 #1
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Here s my take on it :

 

f( ? ) is defined only from  -8 thru 4     so the ? has to equate to this interval

 

f(2x-1)     must fit in the interval      2x-1 must not go outside of the interval

    so  2x-1 = - 8     means x = - 3.5

           2x-1 = 4     means   x = 2.5

 

so as far as I can say (I could be wrong)    the domain of g(x) = [-3.5,2.5]

 May 10, 2021

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