# SOLUTION: whAT IS THE INVERSE OF THE ONE TO ONE FUNCTION f(X)= 6X-7 DIVIDED BY 5

Algebra ->  Algebra  -> Equations -> SOLUTION: whAT IS THE INVERSE OF THE ONE TO ONE FUNCTION f(X)= 6X-7 DIVIDED BY 5      Log On

 Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations! Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

 Algebra: Equations Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on Equations Question 250480: whAT IS THE INVERSE OF THE ONE TO ONE FUNCTION f(X)= 6X-7 DIVIDED BY 5Answer by Theo(3458)   (Show Source): You can put this solution on YOUR website!f(x) = (6x-7)/5 In this equation, solve for x. multiply both sides of the equation by 5 to get: 5 * f(x) = 6x - 7 add 7 to both sides of this equation to get: 5 * f(x) + 7 = 6x divide both sides of this equation by 6 to get: (5 * f(x) + 7) / 6 = x replace x with f(x) and replace f(x) with x (interchange them). equation becomes: (5 * x + 7) / 6 = f(x) that's the same as: f(x) = (5 * x + 7) / 6 that's your inverse function. graph both equation to see that they are symmetric about the line y = x. the graph looks like the lines are symmetric and reflections of each other about the line y = x so it appears that these are inverse functions. test a point to see if they are symmetric about the line y = x. If so, then the point (x,y) in one equation should be equal to the point (y,x) in the other equation. try x = -15 the first equation. at x = -15, y = (6x-7)/5 = -18 (x,y) = (-15,-18) in the first equation. let x = -18 in the second equation. This is the value of y in the first equation. at x = -18, y (5 * -18 / 6) = -15. This is the value of x in the first equation. (y,x) = (-18,-15) in the second equation. the point (x,y) = (-15,-18) in the first equation is equal to the point (y,x) = (-18,-15) in the second equation so the lines are symmetric about the line y = x. in the equations above, if you let y = f(x), then where I have used y you can substitute f(x), and where I have used f(x) you can substitute y, as necessary, in order to put the equation in the form that you need. They both mean the same thing.