Question 250480
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.


{{{graph (600,600,-20,20,-20,20,x,(5 * x + 7) / 6,(6x-7)/5)}}}


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.