Question

Find the inverse of the following. select all that apply ​

Answer 1

`h^(- 1) (x) = \sqrt{(x - 8)^(3)} = (√(x - 8))^(3) = (x - 8)^{(3)/(2) }`

Explanation:

The given function is
`h(x) = \sqrt[3]{x^(2)} + 8` and we have to find the inverse function of this function h(x).

Now, let us assume,
`y = \sqrt[3]{x^(2)} + 8`

⇒
`y - 8 = \sqrt[3]{x^(2)}`

⇒
`(y - 8)^(3) = x^(2)` {Cubing both sides}

⇒ x² = (y - 8)³

⇒
`x = \sqrt{(y - 8)^(3) }`

Therefore, the inverse function
`h^(- 1) (x) = \sqrt{(x - 8)^(3)} = (√(x - 8))^(3) = (x - 8)^{(3)/(2) }`

So, options A, B, and D are correct. (Answer)