Question

Find the inverse of the function f(x)= 6x^3-8

Answer 1

To find the inverse, interchange the variables and solve for
y
y
.
f
−
1
(
x
)
=
√
2
(
x
+
8
)
6
,
−
√
2
(
x
+
8
)
6

Answer 2

Hello, please consider the following.

`(\forall x \in \mathbb{R}) \\ \\ x=(f^(-1)of)(x)\\\\=(fof^(-1))(x)\\\\=f(f^(-1)(x))\\\\=6\left( f^(-1)(x) \right) ^3-8 = x\\\\\text{We need to express }f^(-1)(x) \text{ in function of x.}\\\\\text{Let's do it!}`

`6\left( f^(-1)(x) \right) ^3-8 = x\\\\\left( f^(-1)(x) \right) ^3 =(x+8)/(6)\\\\\Large \boxed{\sf \bf \ \ f^(-1)(x)=\sqrt[3]{(x+8)/(6)}\ \ }`

Thank you