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14 June, 09:23

Determine the domain of the function, and choose the correct interval and inequality notations,

P (x) = 2x+8

Interval notation: (-

notation: (-

Inequality

) U (

why oo)

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Answers (1)
  1. 14 June, 11:20
    0
    See below

    Explanation:

    Determining the domain of the function P (x) = 2x + 8 is very trivial and does not require the uses of separate intervals.

    The domain of a function is the set of input values (x) for which the function is defined. Thus, the domain of P (x) = 2x + 8 is all the real number, which in interval notaion is:

    ( - ∞, ∞)

    The symbol ∞ is used to indicate that there is not limit for the value of x: it can goe from any negative number to any positive number).

    For didactic purposes let's determine the domain of the function

    P (x) = 2 / (x+8).

    In this case, the function is not defined when the denominator equals 0.

    Then, the domain excludes the values for which x + 8 = 0.

    x + 8 = 0 ⇒ x = - 8.

    Then, the solution is all the real numbers different to - 8.

    In interval notation it is:

    ( - ∞, - 8) ∪ (-8, ∞)

    In form of inequaliy that is:

    x - 8

    That means, all the real numbers less than - 8 and all the real numbers greater than 8.
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