Question 11800
I'm assuming that you mean {{{f(x) = (2-4x)/(1-5x) }}}???


If so, start with {{{y = (2-4x)/(1-5x) }}}


The inverse function can be obtained by two steps:
Step 1:  Interchange the x and the y.
Step 2:  Solve for y.  The y that you solve for is actually the inverse function.  Of course, step 2 will probably take several steps to accomplish.


Step 1:  Interchange the x and y.  Change the x's into y's and the y to x:  {{{x = (2-4y)/(1-5y) }}}


Step 2:  Solve for y.  To get started on this, multiply both sides by the common denominator, which is {{{1-5y}}}.

{{{(1-5y)*x = (2-4y) }}}
{{{x- 5xy = 2 - 4y}}}


Get all the y terms on the left side, by adding +4y to each side:
{{{x-5xy + 4y = 2 -4y + 4y}}}

{{{x - 5xy + 4y = 2 }}}


Get all NON-y terms to the right side by subtracting x from each side:
{{{x -x - 5xy + 4y = 2 - x}}}
{{{-5xy + 4y = 2 - x}}}


To get the y in one place, factor out the y:
{{{y(-5x + 4) = 2-x }}}


Divide both sides by (-5x + 4):


{{{(y(-5x+ 4))/(-5x + 4) = (2 - x)/(-5x + 4) }}}


{{{ y = (2-x) /(-5x + 4)}}}


There are several ways to write this that might be even better:
{{{y = (-x+ 2) /(-5x+4)}}} or multiply numerator and denominator by -1:
{{{y = (x-2)/(5x-4)}}} This would be the preferred answer!!


R^2 at SCC