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mel-nik [20]
2 years ago
9

Find the inverse please and thank you

Mathematics
1 answer:
Amanda [17]2 years ago
5 0

The inverse f^{-1}(x) is such that

f\left(f^{-1}(x)\right) = x

We have

f\left(f^{-1}(x)\right) = -9\sqrt{f^{-1}(x) - 8} + 5 = x

Solve for the inverse.

-9\sqrt{f^{-1}(x)-8} + 5 = x \\\\ -9\sqrt{f^{-1}(x)-8} = x-5 \\\\ \sqrt{f^{-1}(x)-8} = -\dfrac{x-5}9 \\\\ \left(\sqrt{f^{-1}(x)-8}\right)^2 = \left(-\dfrac{x-5}9\right)^2 \\\\ f^{-1}(x) - 8 = \dfrac{(x-5)^2}{81} \\\\ \boxed{f^{-1}(x) = 8 + \dfrac{(x-5)^2}{81}}

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