Question

Find the inverse of the function.

f(x) = 6x3 - 8

Answer 1

Replace f(x)fx with yy.y=6x3−8y=6x3-8Interchange the variables.x=6y3−8x=6y3-8Solve for yy.
y=3√36(x+8)6y=36x+836Solve for yy and replace with f−1(x)f-1x.
f−1(x)=3√36(x+8)6

Answer 2

`f^(-1)(x) = \sqrt[3]{(x+8)/(6)}`

Explanation:

Given function,

`f(x)=6x^3-8`

Replace f(x) by y,

`y=6x^3-8`

Switch x and y,

`x=6y^3-8`

Isolate y in the left side,

`-6y^3=-x-8`

`6y^3=x+8`

`y^3=(x+8)/(6)`

`y=\sqrt[3]{(x+8)/(6)}`

Replace y by
`f^(-1)(x)`

`\implies f^(-1)(x) = \sqrt[3]{(x+8)/(6)}`

Which is the required inverse of the given function.