Question

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

Answer 1

Answer:

$h^{- 1} (x) = \sqrt{(x - 8)^{3}} = (\sqrt{x - 8})^{3} = (x - 8)^{\frac{3}{2} }$

Step-by-step 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 $h^{- 1} (x) = \sqrt{(x - 8)^{3}} = (\sqrt{x - 8})^{3} = (x - 8)^{\frac{3}{2} }$

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