Question

If

f(x) = 2x3 + 6, which function satisfies
(fof-1) (x) = x and
(f-10 f)(x) = x? (1 point)

Answer 1

Both are true.

Explanation:

If f(x) = 2x³ + 6

To find the inverse of the given function,

Rewrite the function in the form of an equation,

y = 2x³ + 6

Interchange the variables x and y,

x = 2y³ + 6

Solve for y,

2y³ = x - 6

y =
`\sqrt[3]{((x-6))/(2)}`

Rewrite the equation in the form of a function,

`f^(-1)(x)={\sqrt[3]{((x-6))/(2)}`

`(fof^(-1))(x)=f[f^(-1)(x)]`

=
`2(\sqrt[3]{((x-6))/(2)})^3+6`

= (x - 6) + 6

= x

`(f^(-1)of)(x)=f^(-1)[{f(x)]`

`={\sqrt[3]{((2x^3+6-6))/(2)}`

`={\sqrt[3]{((2x^3))/(2)}`

= x

Therefore, both the statements are true.