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

If f(x) = 2/3x + 9, find f^-1(x)-example-1
User Cosmin SD
by
7.8k points

1 Answer

4 votes

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


f(x) = \frac23x+9

then


f\left(f^(-1)(x)\right) = \frac23f^(-1)(x) + 9 = x

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


\frac23f^(-1)(x)+9 = x \\\\ \frac23f^(-1)(x) = x-9 \\\\ f^(-1)(x) = \frac32(x-9) = \frac32x-\frac{27}2

which makes D the correct answer.

User Iibrahimbakr
by
7.6k points

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