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9 March, 02:22

Explain why f (x) = 1 / (x-3) ^3 is not continuous at x=3

a) f is not defined at x = - 3

b) f is not defined at x = 3

c) f is not defined at x = 0

d) f is not defined at x = 9

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  1. 9 March, 02:24
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    F (x) = 1 / (x-3) ^3

    The denominator can't be equal to zero (we can't divide by zero), then:

    (x-3) ^3 different 0

    cubic root both sides:

    cubic root [ (x-3) ^3 ] different cubic root (0)

    x-3 different 0

    Adding 3 both sides:

    x-3+3 different 0+3

    x different 3

    Then the function f is not defined at x=3

    Answer: Option b) f is not defined at x = 3
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