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kifflom [539]
2 years ago
9

If f(x) = 2/3x + 9, find f^-1(x)

Mathematics
1 answer:
larisa86 [58]2 years ago
6 0

If f^{-1}(x) is the inverse of

f(x) = \dfrac23x+9

then

f\left(f^{-1}(x)\right) = \dfrac23f^{-1}(x) + 9 = x

Solve for f^{-1}(x) :

\dfrac23f^{-1}(x)+9 = x \\\\ \dfrac23f^{-1}(x) = x-9 \\\\ f^{-1}(x) = \dfrac32(x-9) = \dfrac32x-\dfrac{27}2

which makes D the correct answer.

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