Question 1032450
Outline for finding the inverse:
Step 1) Replace f(x) with y
Step 2) Swap x and y
Step 3) Solve for y


Let's follow that outline


{{{f(x) = 3x-6}}} Start with the original equation


{{{y = 3x-6}}} Replace f(x) with y (see step 1 above)


{{{x = 3y-6}}} Swap x and y (see step 2 above)


Now we solve for y (step 3 above). To do this, we first add 6 to both sides to undo the subtraction of 6. Then we undo the multiplication of 3 by dividing both sides by 3.


{{{x = 3y-6}}}


{{{x+6 = 3y-6+6}}} Add 6 to both sides


{{{x+6 = 3y}}}


{{{3y = x+6}}}


{{{(3y)/3 = (x+6)/3}}} Divide both sides by 3.


{{{y = (x+6)/3}}}


So the inverse function is *[Tex \LARGE f^{-1}(x) = \frac{x+6}{3}] which is the final answer.