find the inverse of F(x)=4x^3 -8

`f(x) = 4x^3-8`

To determine its inverse, replace the f(x) with y.

`y=4x^3 -8`

Swap the x and y.

`x=4y^3-8`

Then, isolate the y.

`x+8=4y^3`

`(x+8)/4=y^3`

`root(3)((x+8)/4)=y`

And replace the y with `f^(-1)(x)` .

`root (3)((x+8)/4)=f^(-1)(x)`

Therefore, the inverse function of `f(x) =4x^3-8` is `f^(-1)(x) = root(3)((x+8)/4)` .

Comments

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