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Model 2: Jack owns a company that manufactures a product that we’ll call product A. After producing and selling x units of product A, the profit his company made is represented by the cube root function

Write the inverse of the cube root function used to represent the situation in model 2, f(x) = ∛(x+4)^2

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oladayoademosu oladayoademosu · Answer 1 · 2022-03-24T13:51:53+01:00

The inverse of the cube root function used to represent the situation in model is f⁻¹(x) = √x³ - 4

f(x) = ∛(x + 4)²

To find the inverse function, let f(x) = y

So, y = ∛(x + 4)²

Taking the cube of both sides, we have

y³ = [∛(x + 4)²]³

y³ = (x + 4)²

Taking square root of both sides, we have

√y³ = √(x + 4)²

√y³ = (x + 4)

Subtracting 4 from both sides, we have

√y³ - 4 = x + 4 - 4

√y³ - 4 = x

Replacing y with x, we have

√x³ - 4 = y

Replacing y with f⁻¹(x), we have

f⁻¹(x) = √x³ - 4

So, the inverse of the cube root function used to represent the situation in model is f⁻¹(x) = √x³ - 4

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