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Kipish [7]
2 years ago
12

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

Mathematics
1 answer:
Charra [1.4K]2 years ago
4 0

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)

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