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Let f(x)=2/3x-6 what is the inverse function?

1 Answer

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Change f(x) to a y and switch places with y and x as below.

x= (2)/(3) y-6

Solve the equation for y

x + 6 = (2)/(3) y

Multiply each term by the reciprocal of
(2)/(3)

(3)/(2) (x+6) = y

Distribute

(3)/(2) x+9=y

Change y to
f^(-1)(x)

f^(-1)(x)= (3)/(2) x+9
User Jimmt
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