Determine if f(x)= 4x+1/ x-5 and g(x)= 5x-1/ x+4 are inverses of each other. If they are not invereses explain why.
+129839 f(x)= [4x+1] / [x-5] and g(x)= [5x-1] / [x+4]
There is a simple test to determine if these are inverses if f [ g(x)] = g [ f(x) ] = x, then they are inverses....however......we only need one counter-example to show that they are not
If (x, y) is on the function f(x), then the reverse coordinates are on g(x)....
Let's put x = 0 into the first function.....then f(0) = -1/5 ...then the point (0, -1/5) is on the first graph
Then ( -1/5, 0) should be on the second .....but g(-1/5) = -10/19 .....so the coordinates are not reversed and this indicates that the functions are not inverses of each other....!!!
