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9 June, 22:39

What is the inverse of f (x) = (x-2) ^3

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  1. 9 June, 23:21
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    g⁻¹ (x) = 2 + ∛x

    Step-by-step explanation:

    g (x) = (x - 2) ³ Rename g (x) as y

    y = (x - 2) ³

    Solve for x:

    y = (x - 2) ³ Multiply each side by 3

    ∛y = x - 2 Add 2 to each side

    ∛y + 2 = x

    x = ∛y + 2 Switch x and y

    y = ∛x + 2 Rename y as g inverse

    g⁻¹ (x) = 2 + ∛x

    See the graphs of g (x) and g⁻¹ (x) below.

    g (x) is the red line. g⁻¹ (x) is the blue line.

    Each graph reflects the other about the dashed line representing the function y = x.
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