Find domain of logarithmic function f(x)=sqrt(log((3x−x^2)/(2))

Patricia Bean 2022-07-17 Answered
I know that fraction denominator needs to be > 0 , so if denominator is quadractic equation i know how to solve , But since denominator is > 0 , I dont know how to solve , can anyone help me ?
f ( x ) = log ( 3 x x 2 2 )
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Answers (2)

umgangistbf
Answered 2022-07-18 Author has 12 answers
Hints:
You also need to have
log ( 3 x x 2 2 ) 0
for the square root of that function to be defined, and this implies
3 x x 2 2 1 3 x x 2 2
3 x x 2 2 0 x 2 3 x + 2 = ( x 1 ) ( x 2 ) 0.
The quadratic will be less than or equal to zero when exactly one and only one factor 0:
So the domain is, in fact,
x [ 1 , 2 ] ,  alternatively  1 x 2

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Mauricio Mathis
Answered 2022-07-19 Author has 2 answers
it must be
3 x x 2 2 1
this is equivalent to 0 x 2 3 x + 2 and this is equivalent to
0 ( x 1 ) ( x 2 )

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