I know that fraction denominator needs to be &gt; 0 , so if denominator is quadractic equation i know how to solve , But since denominator is &gt; 0 , I dont know how to solve , can anyone help me ? f ( x ) = log ⁡ ( 3 x − x 2 2 )

Question

I know that fraction denominator needs to be &amp;gt; 0 , so if denominator is quadractic equation i know how to solve , But since denominator is &amp;gt; 0 , I dont know how to solve , can anyone help me ?  f      (    x    )    =      log    ⁡          (                        3          x          −                      x            2                          2            )

umgangistbf · Accepted Answer

Hints:You also need to have  log  ⁡      (                  3        x        −                  x          2                    2        )    ≥  0for 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

Mauricio Mathis · Accepted Answer

it must be            3      x      −              x        2              2    ≥  1this is equivalent to   0  ≥      x    2    −  3  x  +  2 and this is equivalent to  0  ≥  (  x  −  1  )  (  x  −  2  )

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

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New Questions in Calculus 1