Question 1149980
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Use parentheses!<br>
The function you show, y = -3x+1/x-5, is {{{y = -3x+1/x-5}}} -- clearly not what you want.<br>
The function you want is y = (-3x+1)/(x-5), which is {{{y = (-3x+1)/(x-5)}}}<br>
One standard way of finding the inverse of a given function is to switch the x and y and solve for the new y:<br>
{{{x = (-3y+1)/(y-5)}}}
{{{x(y-5) = -3y+1}}}
{{{xy-5x = -3y+1}}}
{{{xy+3y = 5x+1}}}  [gather all the terms with y on one side]
{{{y(x+3) = 5x+1}}}
{{{y = (5x+1)/(x+3)}}}<br>
The inverse is<br>
{{{(5x+1)/(x+3)}}}<br>
If you see problems like this often involving inverses of functions like this, note there is a pattern you can use to write the inverse without going through the algebra to find it.<br>
Look at the original function and it inverse:<br>
{{{(-3x+1)/(x-5)}}} and {{{(5x+1)/(x+3)}}}<br>
The coefficient of x in the numerator and the constant in the denominator switch places and change sign; the constant in the numerator and the coefficient of x in the denominator remain unchanged.<br>
In general, the inverse of {{{(ax+b)/(cx+d)}}} is {{{(-dx+b)/(cx-a)}}}<br>