Question

Use algebra to find the inverse of the function [ f(x)=-6 x³-2 ] The inverse function is ( f⁻¹(x)= )

Answer 1

To find the inverse of the function f(x) = -6x³ - 2, follow these steps: Replace f(x) with y, swap the variables x and y, solve for y, divide both sides by 6, and take the cube root of both sides.

Step-by-step explanation:

To find the inverse of the function f(x) = -6x³ - 2, we can follow these steps:

1. Replace f(x) with y to get y = -6x³ - 2.
2. Swap the variables x and y to get x = -6y³ - 2.
3. Solve for y by rearranging the equation: 6y³ = (-x - 2).
4. Divide both sides by 6 to get y³ = (-x - 2) / 6.
5. Take the cube root of both sides to get y = ³√[(-x - 2) / 6].

Therefore, the inverse function is f⁻¹(x) = ³√[(-x - 2) / 6].

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