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20 April, 11:31

Find the inverse of:

1. g (x) = - 3 + 2

2. F (x) = - 2x^3

3. G (n) = 2n^3 - 2

4. g (x) = x^3

5. g (n) = - 1 - n^3

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Answers (1)
  1. 20 April, 13:33
    0
    The inverse is found by first solving for the independent variable (in these questions, either x or n), then switching it with the dependent variable.

    1. g (x) = - 3 + 2 = - 1

    This function is simply a horizontal line (there is no presence of the independent variable x), so it has no inverse.

    2. F (x) = - 2x^3

    Solving for x: - F/2 = x^3

    (-F/2) ^ (1/3) = x

    Switch the variables to get the inverse function:

    F (x) = (-x/2) ^ (1/3)

    3. G (n) = 2n^3 - 2

    G (n) + 2 = 2n^3

    G (n) / 2 + 1 = n^3

    n = [G (n) / 2 + 1]^ (1/3)

    Inverse: G (n) = (n/2 + 1) ^ (1/3)

    4. g (x) = x^3

    [g (x) ]^ (1/3) = x

    Inverse: g (x) = x^ (1/3)

    5. g (n) = - 1 - n^3

    g (n) + 1 = - n^3

    -g (n) - 1 = n^3

    [-g (n) - 1]^ (1/3) = n

    Inverse: g (n) = (-n-1) ^ (1/3)
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