Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 months ago

Please help! How do I answer this college algebra question?

Here's the question: If f(x)=5-2x^3 and f^-1 denotes the inverse function of f, then f^-1 (x)=.

Could someone please break this question down for me. My understanding of functions is shaky at best.

2 Answers

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  • 2 months ago
    Favourite answer

    You have:

    f(x) = 5 - 2x³

    Let's change the f(x) to a y for now:

    y = 5 - 2x³

    To find the inverse, swap the variables and solve for y again:

    x = 5 - 2y³

    x - 5 = -2y³

    5 - x = 2y³

    (5 - x) / 2 = y³

    ∛[(5 - x) / 2] = y

    Rationalizing the denominator:

    y = ∛(5 - x) / ∛2

    y = ∛(5 - x) * ∛2² / ∛2³

    y = ∛(5 - x) * ∛4 / 2

    y = ∛[4(5 - x)] / 2

    y = ∛(20 - 4x) / 2

    Putting this back into function notation:

    f⁻¹(x) = ∛(20 - 4x) / 2

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  • ted s
    Lv 7
    2 months ago

    if y(x) exists and has an inverse then it is x(y).........y = 5 - 2 x³ then x = {( 5 - y) / 2 }^(1/3) is the inverse function

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