Question 1166430
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The solution by the other (newcomer) tutor is incorrect.<br>
Note the given function graphs as a parabola.  The function has an inverse; but the inverse will not be a function.<br>
To find the inverse, switch the x and y and solve for the new y.<br>
{{{x = y^2-5y}}}<br>
To solve for y, you need to complete the square in y.<br>
{{{x = y^2-5y}}}
{{{x = (y^2-5y+25/4)-25/4}}}
{{{x = (y-(5/2))^2-25/4}}}
{{{(y-(5/2))^2 = x+25/4}}}
{{{y-5/2 = (sqrt(x+25/4))}}}  OR  {{{y-5/2 = -(sqrt(x+25/4))}}}<br>
{{{y = (sqrt(x+25/4))+5/2}}}  OR  {{{y = -(sqrt(x+25/4))+5/2}}}<br>