Lois C. answered • 05/09/20
patient, knowledgeable, and effective tutor for secondary mathematics
Start by replacing the f(x) notation with y , then switch the positions for the x and y variables, so we have y = 2x/(x + 7) which then turns into x = 2y/(y + 7 ). Now we write it as a proportion and cross multiply, so we have x(y + 7) = 2y. Now we want to isolate y, but we need to get the y terms together first. So eliminate the ( ) on the left side, so the equation is now xy + 7x = 2y. Now get the y terms on the same side and factor out the y:
xy - 2y = -7x → y(x - 2 ) = -7x. Now divide both sides by (x-2) to isolate y: y = -7x/(x - 2). We finish by replacing the y with inverse function notation: f '(x) = -7x/(x - 2 )
Lois C.
Hello Yalette. Thank you for your response. I know it is confusing when you get different answers for the same problem. I went back and double-checked my work. My answer is correct, although it is not written in the best form. In my solving process, after switching the x and the y positionally, I would have done better to move all of the y terms to the right side instead of the left side ( this would have eliminated some of the minus signs) and so I would have had this instead: 7x = 2y - xy. Now in factoring out the y, we have 7x = y( 2 - x ) and so y ends up equaling 7x/(2- x). This is equivalent to my original answer but looks a little "nicer". If you have studied composition of functions, you can verify this ( which I have done) by inserting the rule of f^-1 into the rule of f to see if it produces x and then insert the rule of f into f^-1 to see if this also produces x. The other answer(s) you received should have the subtraction in the denominator in reverse order. One minor correction on my notation: for the inverse of f, I used f' in my original response whereas I should have used f ^-1.05/09/20
Yalette A.
Awesome thank you :) thanks for the clarification. Great help.05/09/20
Lois C.
Good, I'm glad. (-:05/09/20
Yalette A.
I’ve seen some say: f(x)^-1= 7x/ x-2 Are they wrong then?05/09/20