Question 1097369
<br>The problem:<br>
Given the function {{{y = (5x+4)/(7)}}}, find the inverse.<br>
(1) Algebraic solution: Switch the x and y in the equation and solve for the new y.<br>
{{{y = (5x+4)/(7)}}}
{{{x = (5y+4)/(7)}}}
{{{7x = 5y+4}}}
{{{7x-4 = 5y}}}
{{{(7x-4)/5 = y}}}
or
{{{y = (7x-4)/5}}}<br><br>
(2)Finding the inverse by understanding that the inverse has to "un-do" what the given function does.<br>
Look at the steps of what is done to the input x to get y in the given function:
a) multiply by 5
b) add 4
c) divide by 7<br>
The inverse function has to un-do all that, so it has to do the opposite operations in the opposite order:
a) multiply by 7:  {{{x}}} becomes {{{7x}}}
b) subtract 4:  {{{7x}}} becomes {{{7x-4}}}
c) divide by 5:  {{{7x-4}}} becomes {{{(7x-4)/5}}}<br>
So again we have the same inverse function: {{{(7x-4)/5}}}