Quick Homework Help

# Inverse of f(x)=(x+7)/(x-6)?? ⚑ Flag

by jackson037 at July 20, 2011

Jackson -Find an inverse by taking two steps:Step 1: substitute y for f(x):f(x) = (x+7)/(x-6)y = (x+7)/(x-6)Step 2: state the problem as a function of y instead of x. In other words, solve for x in terms of y:y = (x+7)/(x-6) , now multiply both sides by (x-6)y(x-6) = (x+7) , now distribute yyx - y6 = x + 7 , re-arrange to get x terms on right sidexy - x = 6y + 7 , now factor out xx(y - 1) = 6y + 7 , finally divide both sides by (y - 1)x = (6y + 7)/(y - 1)That is the inverse of the function. Instead of plugging in x to find y, now you can plug in y to find x.  It's that simple!For example, in the original function if x = 7, then y = 14/1 = 14. The ordered pair (x,y) = (7,14)Now try plugging in y = 14 into the inverse function. We should get right back to x = 7:x = (6y + 7)/(y - 1)x = (6*14+7)/(14-1) = 91/13 = 7.Wow it worked!  So, here the ordered pair (y,x) = (14,7) or the exact inverse of the original function.Hope that helps

Steve204 July 20, 2011

One more thing:  Substitute x wherever you see y in the solution given by Steve.  You can do this in the beginning after you  replaced f(x) by y.  The end result is the inverse function is written:y = (6x +7) / (x-1)

kroo_jteague July 20, 2011

James -When you get a chance, take a look at this recent article in Mathematics Teacher.  You will discover the "old way" of doing inverses (swapping the x and y) is totally misleading to students...Inverse Functions: What Our Teachers Didnâ€™t Tell UsFrank C. Wilson, Scott Adamson, Trey Cox and Alan Oâ€™Bryan March 2011, Volume 104, Issue 7, Page 500Abstract: The concept and notation of inverse functionsâ€”often tricky for studentsâ€”become less so when using real-world data and a strategy of solving for the dependent variable.

Steve204 July 20, 2011