Write the inverse of f (x) = 1/9 (x-4) ^2

Question

Mathematics

Uriah

8 March, 04:01

Write the inverse of f (x) = 1/9 (x-4) ^2

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Answers (1)

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Helen Forbes · Answer 1

F (x) does not pass the horizontal line test, so its inverse is not a function.

Write it as y = f (x), then interchange variables and solve for y.

y = (1/9) (x - 4) ²

x = (1/9) (y - 4) ²

9x = (y - 4) ²

±3√x = y - 4

y = 4 ± 3√x

f⁻¹ (x) = 4 ± 3√x