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# 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.

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- llafferLv 72 months agoFavourite 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 sLv 72 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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