Answer:
[tex]h^{- 1} (x) = \sqrt{(x - 8)^{3}} = (\sqrt{x - 8})^{3} = (x - 8)^{\frac{3}{2} }[/tex]
Step-by-step explanation:
The given function is [tex]h(x) = \sqrt[3]{x^{2}} + 8[/tex] and we have to find the inverse function of this function h(x).
Now, let us assume, [tex]y = \sqrt[3]{x^{2}} + 8[/tex]
⇒ [tex]y - 8 = \sqrt[3]{x^{2}}[/tex]
⇒ [tex](y - 8)^{3} = x^{2}[/tex] {Cubing both sides}
⇒ x² = (y - 8)³
⇒ [tex]x = \sqrt{(y - 8)^{3} }[/tex]
Therefore, the inverse function [tex]h^{- 1} (x) = \sqrt{(x - 8)^{3}} = (\sqrt{x - 8})^{3} = (x - 8)^{\frac{3}{2} }[/tex]
So, options A, B, and D are correct. (Answer)
