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

Answer:

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

Step-by-step 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,

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

$6y^3=x+8$

$y^3=\frac{x+8}{6}$

$y=\sqrt[3]{\frac{x+8}{6}}$

Replace y by $f^{-1}(x)$

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

Which is the required inverse of the given function.