Question 1209327
<pre>
This is the graph of f(x)

{{{drawing(400,400,-6,14,-10,10,graph(400,400,-6,14,-10,10,(2x + 5)/(x - 4)))}}}

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

Substitute y for f(x)

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

Interchange x and y

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

Solve for y:

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

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

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

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

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

Replace y by f<sup>-1</sup>(x):

{{{matrix(1,2,f^(-1),"(x)")}}}{{{""=""}}}{{{(5+4x)/(x-2)}}}

The green graph below is the graph of f<sup>-1</sup>(x), with the point (1,-9)
circled which shows the answer -9:

{{{drawing(400,400,-6,14,-10,10, circle(1,-9,.2),graph(400,400,-6,14,-10,10,(2x + 5)/(x - 4),(5+4x)/(x-2)))}}}

{{{matrix(1,2,f^(-1),"(1)")}}}{{{""=""}}}{{{(5+4(1))/(1-2)=(5+4)/(-1)=9/(-1)=-9}}}   <---answer

Edwin</pre>