find \: the \: domin \: of \: f(x) = \frac{x {}^{2} { + 5x + 1}^{} }{(x - 2)(x - 3)}

Question

find \: the \: domin \: of \: f(x) =  \frac{x {}^{2}  { + 5x + 1}^{} }{(x - 2)(x - 3)}

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Maria 3 weeks 2021-10-07T12:08:07+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-10-07T12:09:15+00:00

    Answer:

    PLS follow me

    Step-by-step explanation:

    Explanation:

    To find the domain, we will factor the quadratic expression in the square root to get

    F

    (

    x

    )

    =

    (

    x

    2

    )

    (

    x

    3

    )

    .

    Assuming

    F

    :

    R

    R

    , we know that

    (

    x

    2

    )

    (

    x

    3

    )

    0

    . Consider

    x

    <

    2

    : we have

    (

    negative

    )

    (

    negative

    )

    =

    positive

    0

    .

    Consider

    2

    <

    x

    <

    3

    : we have

    (

    positive

    )

    (

    negative

    )

    =

    negative

    <

    0

    .

    Consider

    x

    >

    3

    : we have

    (

    positive

    )

    (

    positive

    )

    =

    positive

    0

    .

    Therefore, the domain of

    F

    is

    x

    (

    ,

    2

    ]

    [

    3

    ,

    )

    .

    For the range of

    F

    , we know that the square root function returns non-negative numbers so we know that the range of

    F

    is

    y

    [

    0

    ,

    )

    .

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