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Math

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hello I need help to do this exercise

Consider the function f (x) = (16 x + 33) / (x +3)
1) Determine its domain Df
2) Solve the equation f (x) = 14
3) Show that for all x in Df: f (x) - 15 = (x-12) / (x +3)
4) deduct the resolution of the inequality f (x)> 15.

Thanks for your help.

  • Math - ,

    1 )

    The domain of a function is the set of all possible input values , which allows the function formula to work.

    The denominator of any fraction cannot have the value zero.

    I this case :

    x + 3

    must be different of zero

    x different of - 3

    Domain:

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

    OR

    all values of x different of - 3


    2 )

    ( 16 x + 33 ) / ( x + 3 ) = 14 Multiply both sides by ( x + 3 )

    16 x + 33 = 14 * ( x + 3 )

    16 x + 33 = 14 x + 14 * 3

    16 x + 33 = 14 x + 42

    16 x - 14 x = 42 - 33

    2 x = 9 Divide both sides by 2

    x = 9 / 2


    3 )

    f ( x ) - 15 =

    ( 16 x + 33 ) / ( x + 3 ) - 15 * ( x + 3 ) / ( x + 3 ) =

    ( 16 x + 33 - 15 x - 15 * 3 ) / ( x + 3 ) =

    ( x + 33 - 45 ) / ( x + 3 ) =

    ( x - 12 ) / ( x + 3 )


    4 )

    ( 16 x + 33 ) / ( x + 3 ) > 15
    Multiply both sides by ( x + 3 )

    16 x + 33 > 15 * ( x + 3 )

    16 x + 33 > 15 x + 15 * 3

    16 x + 33 > 15 x + 45

    16 x - 15 x > 45 - 33

    x > 12

  • Math - ,

    Thanks :)

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